We are given the equation $5x + 4y = 32$ and are asked to find the slope and $y$-intercept. The slope is given as $-\frac{5}{4}$, and the $y$-intercept is given as $(0,8)$. We must check if these values are correct and provide simplified answers if needed.

1. Problem Description

We are given the equation $5x + 4y = 32$ and are asked to find the slope and $y$-intercept. The slope is given as $-\frac{5}{4}$, and the $y$-intercept is given as $(0,8)$. We must check if these values are correct and provide simplified answers if needed.

2. Solution Steps

First, we solve the given equation for $y$ to get the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

$5x + 4y = 32$

$4y = -5x + 32$

$y = -\frac{5}{4}x + \frac{32}{4}$

$y = -\frac{5}{4}x + 8$

From the equation $y = -\frac{5}{4}x + 8$, we see that the slope $m = -\frac{5}{4}$ and the $y$-intercept is $b = 8$.

Thus the slope is $-\frac{5}{4}$.

To write the $y$-intercept as an ordered pair, we write $(0, b)$, so the $y$-intercept is $(0, 8)$.

3. Final Answer

$-\frac{5}{4}$

$(0, 8)$