Find an equation for the line with an x-intercept of 4 and y-intercept of -2

Step-by-step explanation:

The x-intercept exists when y = 0; the coordinate that results from our x-intercept is (4, 0).

The y-intercept exists when x = 0; the coordinate that results from our y-intercept is (0, -2).

We can use these 2 coordinates to find the slope of the line we need to write:

Now we can use that slope along with one of our points to write the equation of the line.  I am going to use the point-slope form, then we will solve it for y to put it into slope-intercept.  Let's use the coordinate (4, 0).  Keep in mind that regardless of which point we choose to use to write our equation, we will get the same equation.

y - 0 = 1/2(x - 4) and

y = 1/2x - 2

That's your equation!