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

Question

Number of crates 2 4 6 8
Cost ($) $25 $45 $65 $85
Which equation represents this situation, where x is the number of crates and y is the cost?

Responses

y−85=10(x−8)
y minus 85 equals 10 left parenthesis x minus 8 right parenthesis

y−4=10(x−45)
y minus 4 equals 10 left parenthesis x minus 45 right parenthesis

y−65=−10(x−6)
y minus 65 equals negative 10 left parenthesis x minus 6 right parenthesis

y−2=−10(x−25)

Answer 1

To find the equation that represents the relation between the number of crates (x) and the cost (y), we need to first recognize that the cost changes linearly as the number of crates increases.

From the table, we can see the cost increases by $10 for each additional crate:

• From 2 to 4 crates, the cost goes from $25 to $45, an increase of $20 for 2 crates (or $10 per crate).
• From 4 to 6 crates, the cost goes from $45 to $65, an increase of $20 (still $10 per crate).
• From 6 to 8 crates, the cost goes from $65 to $85, an increase of $20 (again, $10 per crate).

This gives us a slope of \( m = 10 \).

Using the point-slope form of the equation for a line, which is \( y - y_1 = m(x - x_1) \), we can choose a point from the table (let's take (8, 85)) and write the equation:

1. Using the point (8, 85): \[ y - 85 = 10(x - 8) \]

Thus, the equation that corresponds to the situation is:

y - 85 = 10(x - 8)

So the corresponding response is:

y−85=10(x−8)