The problem asks us to convert the given equation $7x - 2y = -6$ into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Problem Description

The problem asks us to convert the given equation $7x - 2y = -6$ into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Solution Steps

Step 1: Isolate the term with $y$.

Starting with $7x - 2y = -6$, we want to isolate the $-2y$ term. Subtract $7x$ from both sides:

$7x - 2y - 7x = -6 - 7x$

$-2y = -7x - 6$

Step 2: Solve for $y$.

To solve for $y$, divide both sides of the equation by $-2$:

$\frac{-2y}{-2} = \frac{-7x - 6}{-2}$

$y = \frac{-7x}{-2} + \frac{-6}{-2}$

$y = \frac{7}{2}x + 3$

The slope-intercept form of the equation is $y = \frac{7}{2}x + 3$.

3. Final Answer

$y = \frac{7}{2}x + 3$