Manuel builds and sells wooden crates. He made a table to show how much his crates cost.

Which equation represents the situation?

Manuel’s Crates
Crates
2 4 6 8
Cost 25 45 65 85


A.
y – 2 = −10(x – 25)

B.
y – 4 = 10(x – 45)

C.
y – 65 = −10(x – 6)

D.
y – 85 = 10(x – 8)



Answer :

Answer

D.  y – 85 = 10(x – 8)

Explanation

First we are going to find the slope of the line equation that represents the situation. To do it we are using the slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where

[tex]m[/tex] is the slope of the line

[tex](x_{1},y_{1})[/tex] are the coordinates of the first point

[tex](x_{2},y_{2})[/tex] are the coordinates of the second point

From our table we can get the points (2, 25) and (4, 45) so [tex]x_{1}=2[/tex], [tex]y_{1}=25[/tex], [tex]x_{2}=4[/tex], and [tex]y_{2}=45[/tex]. Let's replace the values in our formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{45-25}{4-2}[/tex]

[tex]m=\frac{20}{2}[/tex]

[tex]m=10[/tex]

Now that we have our slope, we are going to use the point slope formula:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Since the slope of our line is positive 10, we can rule out answers A and C.

Since the line of answer B has the numbers 4 and 45, we are going to test the point (4, 45) in our point slope formula:

[tex]y-45=10(x-4)[/tex]   Nope! Answer B is not correct.

Since the line of answer D has the numbers 8 and 85, we are going to test the point (8, 85) in our point slope formula:

[tex]y-85=10(x-8)[/tex]  We got the same line, so D is the correct answer.

Answer:

d is the answer

Step-by-step explanation:

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