Let's begin by figuring out what the slope of the line is. We can do that using this equation:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
If you are subtracting a negative, flip the sign into a positive. This is because a negative times a negative equals a positive.
[tex]m= \frac{-4 + 20}{12 - 6}; m = \frac{16}{6} [/tex]
Now, we can put [tex]m[/tex] into the slope-intercept form, which is this equation:
[tex]y = mx + b[/tex]
Let's input m.
[tex]y=16/6x+b[/tex]
After that, we can select any point for the [tex]x[/tex] and [tex]y[/tex] values, input those, and solve for [tex]b[/tex]. I'll be using (6, -20).
-20 = 16/6(6) + b
Multiply everything out.
-20 = 16 + b
Subtract 16 from both sides.
-36 = b
With this information, we have this:
[tex]y = 16/6x - 36[/tex]
When graphed, that equation looks like the picture I've included below.
The x-intercept is the point that strikes the x-axis, and is (13.5, 0). The y-intercept is the point that strikes the y-axis, and is (0, -36).
