Question

A group of a line is represented by the equation 5x-8y=40. Which value represents the rate of change of y with respect to x for the equation?

Responses:
-8/5
-5/8
5/8
8/5

Answer 1

To determine the rate of change of \( y \) with respect to \( x \) for the equation \( 5x - 8y = 40 \), we can rearrange the equation into slope-intercept form \( y = mx + b \), where \( m \) represents the slope.

Starting with the original equation:

\[
5x - 8y = 40
\]

We can isolate \( y \):

1. Subtract \( 5x \) from both sides:
\[
-8y = -5x + 40
\]

2. Divide every term by \(-8\):
\[
y = \frac{5}{8}x - 5
\]

From this rearrangement, we see that the slope (or the rate of change of \( y \) with respect to \( x \)) is \( \frac{5}{8} \).

Therefore, the value that represents the rate of change of \( y \) with respect to \( x \) is:

\[
\frac{5}{8}
\]

So the correct response is:

**5/8**