We are asked to find the slope of the line given by the equation $5x + 4y = 32$.

1. Problem Description

We are asked to find the slope of the line given by the equation $5x + 4y = 32$.

2. Solution Steps

To find the slope, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

First, we subtract $5x$ from both sides of the equation:

$5x + 4y - 5x = 32 - 5x$

$4y = -5x + 32$

Next, we divide both sides of the equation by $4$:

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

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

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

Comparing this to the slope-intercept form $y = mx + b$, we can identify the slope $m$ as $-\frac{5}{4}$.

3. Final Answer

$-\frac{5}{4}$