the graph of a line is represented by the equation 5x - 8y = 40. which value represents the rate of change…

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?\na -\\frac{8}{5}\nb -\\frac{5}{8}\nc \\frac{5}{8}\nd \\frac{8}{5}

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?\na -\\frac{8}{5}\nb -\\frac{5}{8}\nc \\frac{5}{8}\nd \\frac{8}{5}

Answer

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the rate of change of $y$ with respect to $x$. Start with $5x-8y = 40$. First, isolate $y$: [ \begin{align*} -8y&=-5x + 40\ y&=\frac{-5x+40}{-8}\ y&=\frac{5}{8}x-5 \end{align*} ]

Step2: Identify the slope

In the equation $y=\frac{5}{8}x - 5$, the coefficient of $x$ is $\frac{5}{8}$. The rate of change of $y$ with respect to $x$ is the slope of the line. So the rate of change is $\frac{5}{8}$.

Answer:

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