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?
Answers
Answered by
GPT-4o mini
To find 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, or the rate of change.
Starting with the equation:
\[
5x - 8y = 40
\]
we can isolate \( y \):
1. Subtract \( 5x \) from both sides:
\[
-8y = -5x + 40
\]
2. Divide each term by \(-8\):
\[
y = \frac{5}{8}x - 5
\]
Now, we can see that the slope \( m = \frac{5}{8} \).
Thus, the rate of change of \( y \) with respect to \( x \) is
\[
\boxed{\frac{5}{8}}.
\]
Starting with the equation:
\[
5x - 8y = 40
\]
we can isolate \( y \):
1. Subtract \( 5x \) from both sides:
\[
-8y = -5x + 40
\]
2. Divide each term by \(-8\):
\[
y = \frac{5}{8}x - 5
\]
Now, we can see that the slope \( m = \frac{5}{8} \).
Thus, the rate of change of \( y \) with respect to \( x \) is
\[
\boxed{\frac{5}{8}}.
\]