Question

The graph of a line is represented by the equation
5x−8y=40.What value represents the rate of change of
y with respect to
x for the equation?

Rate of Change:
Correct?
❌

Answer 1

To find the rate of change of \( y \) with respect to \( x \) (which is the slope of the line), we need to rewrite the equation \( 5x - 8y = 40 \) in slope-intercept form (\( y = mx + b \)), where \( m \) is the slope.

Starting with the given equation:

\[
5x - 8y = 40
\]

We can rearrange it to solve for \( y \):

1. Subtract \( 5x \) from both sides:

\[
-8y = -5x + 40
\]

2. Divide every term by \( -8 \):

\[
y = \frac{5}{8}x - 5
\]

In this form, the slope \( m \) is \( \frac{5}{8} \).

Thus, the rate of change of \( y \) with respect to \( x \) is:

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

So the correct answer for the rate of change is:

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

If you marked it incorrect previously, this value should clarify it.