The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C
What is an algebraic expression?An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.
Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;
AdditionSubtractionDivisionBracketMultiplicationParentheses. etcFrom the information given, we have that;
negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15Substitute the values
- 1/7j + 2/5 - 3/2j - 7/15
collect like terms
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15
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help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following information:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)
f(0) = 0+0-0+12
f(0) = 12
Now, to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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A landscape supply business charges $35 to deliver mulch. The cost of the mulch is
$29 per cubic yard. Write a linear equation to find the cost of having x cubic yards of
mulch delivered to a site.
The linear function to represent the number of mulch delivered to a site is y = 29x + 35
What is a linear function?In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c
m = slope
c = intercept
We can use this concept to write a linear function to represent this problem:
y = mx + c
y = 29x + 35
In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.
The equation representing this problem is y = 29x + 35
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May I please get help with this math problem it’s so confusing
We have to find the value of z and x.
We assume that lines g and h are parallel.
Then, z and the angle with measure 85° are consecutive interior angles.
As they are conscutive interior angles, their measures add 180°.
Then, we can write:
[tex]\begin{gathered} z+85\degree=180\degree \\ z=180-85 \\ z=95\degree \end{gathered}[/tex]Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.
Then, we can write:
[tex]\begin{gathered} z=6x-109 \\ 95=6x-109 \\ 95+109=6x \\ 204=6x \\ x=\frac{204}{6} \\ x=34 \end{gathered}[/tex]Answer: z = 95 and x = 34.
An electronics store makes a profit of $59 for everystandard DVD player sold and $69 for every portableDVD player sold. The manager's target is to make atleast $345 a day on sales from standard and portableDVD players. Write an inequality that represents thenumbers of both kinds of DVD players that can besold to reach or beat the sales target. Let s representthe number of standard DVD players sold and prepresent the number of portable DVD players sold.Then graph the inequality.
The profit on one standard DVD player is $59 and on one portable DVD player is $69.
If there are s number of standard DVD player then total profit on standard DVD players is $59s. Simillarly total profit on portable DVD players is $69p.
The total profit on DVD player shoul be at least $345, which means total profit on DVD players is $345 or more than $345.
The linear inequalty for total profit is,
[tex]59s+69p\ge345[/tex]The graph of the linear inequality is,
In graph, lines pointing away the origin represent the region for the equation.
please help this is for my study guide thanks! (find volume) (don't round)
100,000π ft³
1) Let's find the volume of that Cylinder using this formula:
[tex]V=\pi r^2h[/tex]Note that the volume is the area of the base (a circle) times the height
2) Also, notice that in the picture we have the diameter, the radius is half the Diameter:
[tex]\begin{gathered} V=\pi\cdot(50)^2\cdot40 \\ V=100000\pi^{} \end{gathered}[/tex]3) So the volume is 100,000π ft³
Multiply.4y=2y3v2.4v7
Let's recall one of the properties of exponents:
[tex]x^4\ast x^5=x^{4\text{ + 5}}=x^9[/tex]Therefore, in our exercise we have:
[tex]4y\text{ }\ast2y^3=8y^{4\text{ }}andv^2\ast4v^7=4v^9[/tex][tex]8y^4\ast4v^9=32y^4v^9[/tex]Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
See the attached for the math problem
1. If the cake rises by ¹/₃ as it bakes, the number of cups of cake batter needed for the four cakes is 140.
2. If ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides, the number of cups of icing needed for the four cakes is 47.
How are the numbers determined?The number of cups of cake batter and icing can be determined using the mathematical operations of multiplication, addition, division, and subtraction.
First, the volumes of each cake and its batter are calculated using the given dimensions and the rise.
Using the division operation, the number of cups of cake batter for each cake is determined and multiplied by four.
We understand that the normal volume of the cake will increase with the icing, helping us to calculate the increased volume after the icing.
The difference between the two volumes becomes the volume of the icing required, which is divided by 14.4 in³ to get the number of cups of icing required.
a) Cups of Cake Butter:The volume of each cake = Length x Width x Height
Length = 14 inches
Width = 12 inches
Height = 4 inches (2 x 2)
= 12 x 14 x 4
= 672 in³.
Rise of the cake as it bakes = ¹/₃
The normal volume before rising = 1
Risen volume = 1¹/₃
1¹/₃ = 672 in³
The normal volume of cake batter before the ¹/₃ rise = 504 in³ (672/1¹/₃).
1 cup = 14.4 in³, the total cups for each cake = 35 cups (504 in³/14.4 in³).
The total cups of cake batter for the 4 cakes = 140 cups (35 x 4).
b) Cups of Icing:The total quantity of icing = 1¹/₄ (¹/₄ + ¹/₂ + ¹/₂).
The new volume after the icing = 840 in³ (672 x 1¹/₄)
The difference in volume after the icing = 168 in³ in (840 in³ - 672 in³)
If 1 cup = 14.4 in³, the cups of icing for each cake = 11.67 cups (168 in³/14.4 in³).
The total cups of icing for the 4 cakes = 47 cups (11.67 x 4).
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Question Completion:Four double-layered cakes, each 12.0 in. x 14.0 in., have been ordered for a special event. Each layer is 2.0 in. high.
a) If the cake rises by ¹/₃ as it bakes, how many cups of cake batter are needed? (1 cup = 14.4 in³. Hint: The ¹/₃ rise should be treated as a constant.)
b) How many cups of icing are needed if ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides? (Assume icing is not layered on top of the icing. 1 cup = 14.4 in³.)
help in this question
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
A vertex example is what?f(x)=3(x−1)2
Find the given parabola's characteristics.
Lessen the steps you tap...
Vertex form is to be used, y=a(x−h)2+k,
to calculate the values of a, h, and k.
a=3
h=1
k=0
The parabola widens because the value of an is positive.
opens up
Find the (h,k) vertex. ( 1 , 0 )
Calculate p, the distance between the focus and the vertex.
To continue, tap...
1/ 12
Locate your focus.
To continue, tap... ( 1 , 1/ 12 )
By identifying the line that connects the vertex with the focus, you may determine the axis of symmetry.
x = 1
The horizontal line that results from deducting p from the vertex's y-coordinate k depends on whether the parabola opens up or down. This line is known as the directrix.
y = k − p
Simplify the formula after substituting the known p and k values.
y = − 1 /12
Analyze and graph the parabola using its characteristics.
Direction: opens up
vertices: ( 1, 0 )
Focus: ( 1 , 1 /12 )
x = 1 is the symmetry axis.
Direction: y = /1 12.
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Endpoint: (1,3) Midpoint: (-2,5) Please I need help ASAP
2. A wooden cube with volume 64 is sliced in half horizontally. The two halves are then glued together to form a rectangular solid which is not a cube. What is the surface area of this new solid? A.128 B. 112 C. 96 D. 56
we have that
the volume of the cube is equal to
V=b^3
64=b^3
b^3=4^3
b=4 unit
see the attached figure
the surface area of the new figure is equal to
SA=2B+PH
where
B is the area of the base
P is the perimeter of the base
H is the height
we have
B=4*8=32 unit2
P=2(4+8)=24 unit
H=2 unit
so
SA=2(32)+24*2
SA=64+48
SA=112 unit2
the answer is option BHow many liters of paint must you buy to paint the walls of a rectangular prism-shaped room that is 20 m by 10 m with a ceiling height of 8 m if 1 L of paint covers40 m2? (Assume there are no doors or windows and paint comes in 1-L cans.)
17 Liters
Explanation
Step 1
find the total area to paint
we need to assume the floor wont be painted, so the total are to paint is
the are of a rectangle is gieven by:
[tex]Area=length*width[/tex]so, the total area will be
[tex]\begin{gathered} total\text{ surface area=\lparen20*10\rparen+2\lparen20*8\rparen+2\lparen10*8\rparen} \\ total\text{ surface area=200+2\lparen160\rparen+2\lparen80\rparen} \\ total\text{ surface area=200+320+160} \\ total\text{ surface area=680 m}^2 \end{gathered}[/tex]so , the area to paint is 680 square meters
Step 2
finally, to know the number of Liters need , divide the amount ( total area) by the rate of the paitn, so
[tex]\begin{gathered} paint\text{ needed=}\frac{total\text{ area}}{rate\text{ paint}} \\ paint\text{ needed=}\frac{680m^2}{40\frac{m^2}{L}}=17Liters \end{gathered}[/tex]so, the total paint needes is 17 Liters, and paint comes in 1-L cans, so
[tex]\begin{gathered} 17\text{ Liters} \\ 17\text{L}\imaginaryI\text{ters\lparen}\frac{1\text{ Can}}{1\text{ L}})=17cans \end{gathered}[/tex]therefore, the answer is
17 Liters
I hope this helps you
Which pair of numbers are not opposites?
47 and- 47
74 and -74
|4| and -4
47 and |-47|
FOR THE PAIRS TO BE OPPOSITE IT MEANS THE NUMBERS SHOULD ALSO CONTRAST IN SIGNS.
47 AND -47 ARE OPPOSITE
74 AND - 74 ARE OPPOSITE
|4|=4 AND -4 ARR OPPOSITE
47 AND |-47|=47 ARE NOT OPPOSITE BECAUSE THEY BOTH HAVE THE SAME SIGNS.
THE LAST OPTION IS THE ANSWER.
please answer this question
Answer:
3
Step-by-step explanation:
Given expression:
[tex]\dfrac{(14^2-13^2)^{\frac{2}{3}}}{(15^2-12^2)^{\frac{1}{4}}}[/tex]
Following the order of operations, carry out the operations inside the parentheses first.
Apply the Difference of Two Square formula [tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
to the operations inside the parentheses in both the numerator and denominator:
[tex]\implies \dfrac{((14+13)(14-13))^{\frac{2}{3}}}{((15+12)(15-12))^{\frac{1}{4}}}[/tex]
Carry out the operations inside the parentheses:
[tex]\implies \dfrac{((27)(1))^{\frac{2}{3}}}{((27)(3))^{\frac{1}{4}}}[/tex]
[tex]\implies \dfrac{(27)^{\frac{2}{3}}}{(81)^{\frac{1}{4}}}[/tex]
Carry out the prime factorization of 27 and 81.
Therefore, rewrite 27 as 3³ and 81 as 3⁴:
[tex]\implies \dfrac{(3^3)^{\frac{2}{3}}}{(3^4)^{\frac{1}{4}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^{(3 \cdot \frac{2}{3})}}{3^{(4 \cdot \frac{1}{4})}}[/tex]
[tex]\implies \dfrac{3^2}{3^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(2-1)}[/tex]
[tex]\implies 3^1[/tex]
[tex]\implies 3[/tex]
Given that,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
Evaluating the problem,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
→ ((196 - 169)^⅔)/((225 - 144)^¼)
→ (27^⅔)/(81^¼)
→ ((3³)^⅔)/((3⁴)^¼)
→ (3²)/3
→ 9/3 = 3
Therefore, the solution is 3.
The half-life of a radioactive isotope is the time it takes for quantity of the isotope to be reduced to half its initial mass. Starting with 175 grams of a radioactive isotope, how much will be left rafter 5 half-lives? Round your answer to the nearest gram
Exponential Decay
The model for the exponential decay of a quantity Mo is:
[tex]M=M_o\cdot e^{-\lambda t}[/tex]Where λ is a constant and t is the time.
The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:
[tex]\begin{gathered} \frac{M_o}{2}=M_o\cdot e^{-\lambda t} \\ \text{Simplifying:} \\ e^{-\lambda t}=\frac{1}{2} \\ \text{Taking natural log:} \\ -\lambda t=-\log 2 \\ t=\frac{\log 2}{\lambda} \end{gathered}[/tex]It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.
Substituting in the model:
[tex]M=175gr\cdot e^{-\lambda\cdot\frac{5\log 2}{\lambda}}[/tex]Simplifying (the value of λ cancels out):
[tex]\begin{gathered} M=175gr\cdot e^{-5\log 2} \\ \text{Calculating:} \\ M=175gr\cdot0.03125 \\ M=5.46875gr \end{gathered}[/tex]Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.
Find the slope of the line defined by each pair of points.:( points :(-1,4). Points. (-1,-5)
Notice that the x coordinate of both points is the same, therefore the line is a vertical line.
Answer: The slope is undefined.
2. Factor completely
2x^2 + 8x + 6
The factors are -3 and -1
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
2x² + 8x + 6
Put it equal to 0 so that we can solve for 'x'
2x² + 8x + 6 = 0
Now, its factors are 6x and 2x
2x² + 6x + 2x + 6 = 0
2x(x + 3) + 2(x + 3) = 0
To cross check your solution is correct or not. You've to just see the the brackets value should be same after taking common. Here the bracket value is (x+3) which is same.
(2x + 2) (x+3) = 0
split the values to solve further,
2x + 2 = 0 | x + 3 = 0
2x = -2 | x = -3
x = -2/2
x = -1
Hence, the factors are -3 and -1
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The width of a rectangle is 6x + 8 and the length of the rectangle is 12x + 16 determine the ratio of the width to the perimeter.Supply the following:Perimeter = 21 + 2w = Ratio= w/p Final answer in simplest form:
Solution:
For this case we know that the width is given by:
w = 6x +8
The lenght is given by:
l= 12x +16
And the perimeter would be given by:
P= 2l +2w = 2(12x+16)+ 2(6x+8)= 24x+32 +12x+16=36x + 48
And then the ratio would be:
[tex]\text{ratio}=\frac{6x+8}{36x+48}=\frac{3x+4}{18x+24}[/tex]Choose the equation below that represents the line passing through the point (2, -4) with a slope of(1 point)Oy=kx-3Oy -x+5Oy-1x+3Oy=1x-5
The equation of a line in slope-intercept form can be written like this:
y = mx + b
Where m is the slope and b is the y-intercept of the line.
In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:
y = (1/2)x + b
We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:
-4 = 2(1/2) + b
-4 = 1 + b
-4 - 1 = 1 - 1 + b
-5 = b
b = -5
Then, we can rewrite the equation of the line, like this:
y = (1/2)x - 5
Then, the last option is the correct answer
The illustration below shows the graph of y as a function of x.complete the following sentences based on the graph of the function.* initially, as x increases, y (increases, decreases or stays constant).* the slope of the graph is equal to ___ for all x between x = 0 and x = 3.* starting at x = 3, the function value y (increases, decreases, or stays constant) as x increases.* the slope of the graph is equal to ___ for x between x = 3 and x = 5.* for x between x = 0 and x = 4, the function value y (≤, ≥, or =) 0.* for x between x = 4 and x = 8, the function value y (≤, ≥, or =) 0.
We will have the following:
*Initially, as x increases, y decreases.
*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.
*Starting at x = 3, the function value y increases as x increases.
*The slope of the graph is equal to 3 for x between x = 3 & x = 5.
*For x between x = 0 & x = 4, the function value y ≤ 0.
*For x between x = 4 & x = 8, the function value y ≥ 0.
Teresa is participating in a 4day cross-country bike challenge. She biked it for 61, 67, and 66 miles on the first three days. How many miles does she need to bike on the last day so that her average (mean) is 63 miles per day?
The number of miles that she need to bike on the last day so that her average (mean) is 63 miles per day is 62 miles.
What is a mean?The mean is the average of a set of numbers. Let the biking of the last day be represented as x. This will be:
(61 + 67 + 66 + x) / 4 = 64
(194 + x) / 4 = 64
Cross Multiply
194 + x = 64 × 4
194 + x = 256
Collect like terms
x = 256 - 194
x = 62
The miles is 62 miles.
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Solve the following and give the interval notation of the solution and show the solution on a number line. 6x-12(3-x) is less than or equal to 9(x-4)+9x
The Solution:
The given inequality is
[tex]6x-12(3-x)\leq9(x-4)+9x[/tex]Clearing the brackets, we get
[tex]6x-36+12x\leq9x-36+9x[/tex]Collecting the like terms, we get
[tex]\begin{gathered} 6x+12x-9x-9x\leq-36+36 \\ \end{gathered}[/tex][tex]\begin{gathered} 18x-18x\leq0 \\ 0\leq0 \end{gathered}[/tex]So, the solution is true for all real values of x.
The interval notation of the solution is
[tex](-\infty,\infty)[/tex]parallelogram pqrs has diagonals PR in SQ that intersect at T given s p equals 2 a + 5 + r q equals 5 a - 1 St equals 3 b - 3 + SQ equals 7 b - 9 what are the values of RQ and TQ
SP = 2a+5
RQ= 5a-1
ST = 3b-3
SQ = 7b-9
RQ=?
TQ=?
SP = RQ
2a+5 = 5a-1
Solve for a
5+1 = 5a-2a
6 = 3a
6/3 = a
2=a
RQ= 5a-1 = 5(2)-1 = 10-1 = 9
RQ= 9
ST + TQ = SQ
ST= TQ
TQ= 3b-3
3b-3+3b-3= 7b-9
Solve for b
6b-6 = 7b-9
-6+9 = 7b-6b
3=b
TQ = 3b-3= 3(3)-3= 9-3 =6
TQ= 6
If 12 gallons of gas cost $26.68, howmuch will 15 gallons cost? (proportion)
It is expected that the cost of gas will increase as the number of gallons increases and decrease as the number of gallons decrease. This is a direct proportion
As such, if
12 gallons of gas cost $26.68
15 gallons will cost 15/12 * $26.68
= $33.35
15 gallons of gas will cost $33.35
Can you please help me out with a question
S = 2(a*b + a*c + b*c)
= 2 (12*15 + 12*6 + 15*6)
= 2 (342)
= 684 ft^2
Which of the following are equations for the line shown below? Check all that apply. 5 (1,2) (3-6) I A. y + 6 = -4(x-3) B. y + 3 = -4(X-6) I C. y1 = -4(x-2) D. y - 2 = -4(x - 1)
We have the next points (1,2) and (3,-6)
Evaluate g(-3)Determine the coordinates of the point given by the answer aboveEvaluate g(2a)Step By Step Explanation Please
Given the quadratic equation:
[tex]g(x)=3x^2-5x+4[/tex]Let's solve for the following:
• (a) g(-3)
To solve for g(-3), substitute -3 for x and evaluate.
Thus, we have:
[tex]\begin{gathered} g(x)=3x^2-5x+4 \\ \\ g(-3)=3(-3)^2-5(-3)+4 \\ \\ g(-3)=3(9)+15+4 \\ \\ g(-3)=27+15+4 \\ \\ g(-3)=46 \end{gathered}[/tex]Hence, we have:
g(-3) = 46
• (b) To determine the coordinates of the point given in question (a).
In the function, g(x) can also be written as y.
Thus, from g(-3), we have the following:
x = -3
y = 46
When x = -3, the value of y = 46
In point form, we have the coordinates:
(x, y) ==> (-3, 46)
Therefore, the coordinates of the given point by the answer in (a) is:
(-3, 46)
• (c) Evaluate g(2a).
To evaluate g(2a), substitute 2a for x in the equation and evaluate.
Thus, we have:
[tex]\begin{gathered} g(x)=3x^2-5x+4 \\ \\ g(2a)=3(2a)^2-5(2a)+4 \\ \\ g(2a)=3(4a^2)-5(2a)+4 \\ \\ g(2a)=12a^2-10a+4 \end{gathered}[/tex]ANSWERS:
• (a) g(-3) = 46
• (b) (-3, 46)
• (c) g(2a) = 12a² - 10a + 4
I need help on thisChange the equation into a equivalent equation written in the Slope-intercept form. x -7y + 5 =0
The slope-intercept form is an equation as follows:
[tex]y=mx+b[/tex]Then, we need to change the original equation in this equivalent:
[tex]-7y=-5-x\Rightarrow-7y=-x-5\Rightarrow7y=x+5[/tex]Dividing the total equation by 7, we have:
[tex]\frac{7}{7}y=\frac{x}{7}+\frac{5}{7}\Rightarrow y=\frac{1}{7}x+\frac{5}{7}[/tex]Therefore, the slope-intercept form is:
[tex]y=\frac{1}{7}x+\frac{5}{7}[/tex]I need to find two sets of coordinates and graph them. Please help?!
Answer
The two coordinates on the line include
(0, -1.5) and (-4.5, 0)
The graph of the line is presented below
Explanation
We are asked to plot the grap of the given equation of a straight line.
To do that, we will obtainthe coordinates of two points on the line.
These two points will preferrably be the intercepts of the line.
y = (-x/3) - (3/2)
when x = 0
y = 0 - (3/2)
y = -(3/2)
y = -1.5
First coordinate and first point on the line is (0, -1.5)
when y = 0
0 = (-x/3) - (3/2)
(x/3) = -(3/2)
x = (-3) (3/2)
x = -(9/2)
x = -4.5
Second coordinate and second point on the line is thus (-4.5, 0)
So, to plot the line, we just mark these two points and connect them to each other.
The graph of this line is presented under 'Answer' above.
Hope this Helps!!!