Question

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 1

d is the answer

Explanation:

i took the quiz and got it right

Answer 2

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:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

where

`m` is the slope of the line

`(x_(1),y_(1))` are the coordinates of the first point

`(x_(2),y_(2))` are the coordinates of the second point

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

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(45-25)/(4-2)`

`m=(20)/(2)`

`m=10`

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

`y-y_(1)=m(x-x_(1))`

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:

`y-45=10(x-4)` 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:

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