Question
a 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 \( x \) in the equation \( 5x - 8y = 40 \), we can rewrite this equation in slope-intercept form, \( y = mx + b \), where \( m \) represents the slope of the line.
Starting with the equation:
\[
5x - 8y = 40
\]
we can isolate \( y \):
1. Subtract \( 5x \) from both sides:
\[
-8y = -5x + 40
\]
2. Now, divide every term by \(-8\):
\[
y = \frac{5}{8}x - 5
\]
From the equation \( y = \frac{5}{8}x - 5 \), we see that the slope \( m \), which represents the rate of change of \( y \) with respect to \( x \), is:
\[
\frac{5}{8}
\]
Thus, the rate of change of \( y \) with respect to \( x \) for the equation \( 5x - 8y = 40 \) is \( \frac{5}{8} \).
Starting with the equation:
\[
5x - 8y = 40
\]
we can isolate \( y \):
1. Subtract \( 5x \) from both sides:
\[
-8y = -5x + 40
\]
2. Now, divide every term by \(-8\):
\[
y = \frac{5}{8}x - 5
\]
From the equation \( y = \frac{5}{8}x - 5 \), we see that the slope \( m \), which represents the rate of change of \( y \) with respect to \( x \), is:
\[
\frac{5}{8}
\]
Thus, the rate of change of \( y \) with respect to \( x \) for the equation \( 5x - 8y = 40 \) is \( \frac{5}{8} \).
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