The problem requires us to find the equation of a line given its slope and y-intercept, and to express the equation in slope-intercept form. We are given the slope $m = \frac{4}{7}$ and the y-intercept $(0, -2)$. The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-coordinate of the y-intercept.

1. Problem Description

The problem requires us to find the equation of a line given its slope and y-intercept, and to express the equation in slope-intercept form. We are given the slope $m = \frac{4}{7}$ and the y-intercept $(0, -2)$. The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-coordinate of the y-intercept.

2. Solution Steps

We are given the slope $m = \frac{4}{7}$ and the y-intercept $(0, -2)$, so $b = -2$.

The slope-intercept form of a linear equation is

$y = mx + b$

Substituting the given values:

$y = \frac{4}{7}x + (-2)$

$y = \frac{4}{7}x - 2$

3. Final Answer

$y = \frac{4}{7}x - 2$