We are asked to find the equation of a line given its slope and y-intercept. The slope is $\frac{4}{7}$ and the y-intercept is $(0, -3)$. We need to express the equation in slope-intercept form.

1. Problem Description

We are asked to find the equation of a line given its slope and y-intercept. The slope is $\frac{4}{7}$ and the y-intercept is $(0, -3)$. We need to express the equation in slope-intercept form.

2. Solution Steps

The slope-intercept form of a linear equation is given by:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

In our case, we have $m = \frac{4}{7}$ and $b = -3$.

Substituting these values into the slope-intercept form, we get:

$y = \frac{4}{7}x - 3$

3. Final Answer

$y = \frac{4}{7}x - 3$