1. The problem is to graph the line with slope 4 and y-intercept -2. 2. The formula for a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Here, $m = 4$ and $b = -2$, so the equation of the line is $$y = 4x - 2$$. 4. To graph this line, start at the y-intercept point $(0, -2)$ on the coordinate plane. 5. From the y-intercept, use the slope to find another point. Since the slope is 4, it means rise over run is $\frac{4}{1}$, so go up 4 units and right 1 unit to reach the point $(1, 2)$. 6. Draw a straight line through the points $(0, -2)$ and $(1, 2)$ extending in both directions. This line represents all points $(x, y)$ that satisfy the equation $$y = 4x - 2$$.