Question

1. 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?

options: ( -\frac{8}{5} ), ( -\frac{5}{8} ), ( \frac{5}{8} ), ( \frac{8}{5} )

Explanation:

Step1: Rearrange to slope-intercept form

Start with the given equation:
$$5x - 8y = 40$$
Subtract $5x$ from both sides:
$$-8y = -5x + 40$$

Step2: Isolate y to find slope

Divide all terms by $-8$:
$$y = \frac{-5x}{-8} + \frac{40}{-8}$$
Simplify the expression:
$$y = \frac{5}{8}x - 5$$
The coefficient of $x$ is the rate of change.

Answer:

$\frac{5}{8}$ (corresponding to the second option: $\boldsymbol{\frac{5}{8}}$)