We are given the equation $5x + 2y = 12$ and asked to find the slope of the line.

1. Problem Description

We are given the equation $5x + 2y = 12$ and asked to find the slope of the line.

2. Solution Steps

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

We have $5x + 2y = 12$.

Subtract $5x$ from both sides:

$2y = -5x + 12$.

Divide both sides by 2:

$y = \frac{-5}{2}x + \frac{12}{2}$.

Simplify:

$y = -\frac{5}{2}x + 6$.

From the slope-intercept form, we can identify the slope as the coefficient of $x$, which is $-\frac{5}{2}$.

3. Final Answer

$-\frac{5}{2}$