Question

the graph 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?
a -\frac{8}{5}
b -\frac{5}{8}
c \frac{5}{8}
d \frac{8}{5}

Explanation:

Step1: Rewrite equation in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the rate of change of $y$ with respect to $x$. Starting with $5x−8y = 40$, we solve for $y$. First, subtract $5x$ from both sides: $-8y=-5x + 40$.

Step2: Isolate $y$

Divide each term by $-8$: $y=\frac{5}{8}x-5$.

Answer:

C. $\frac{5}{8}$