The problem asks to find the y-intercept of the equation $5x + 2y = 12$. We are given that the slope is $-\frac{5}{2}$.

1. Problem Description

The problem asks to find the y-intercept of the equation $5x + 2y = 12$. We are given that the slope is $-\frac{5}{2}$.

2. Solution Steps

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

Starting with the given equation $5x + 2y = 12$, we need to isolate $y$ on one side of the equation.

First, subtract $5x$ from both sides:

$2y = -5x + 12$

Next, divide both sides by 2:

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

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

Now, we can see that the slope $m = -\frac{5}{2}$ and the y-intercept $b = 6$. The y-intercept is the point where the line crosses the y-axis, which occurs when $x = 0$. Therefore, the y-intercept as an ordered pair is $(0, 6)$.

3. Final Answer

$(0, 6)$