Question

Determine the x and y intersepts of the line that passes through the following points. (6,-20) (9,-120 (12,-4)

Answer 1

Let's begin by figuring out what the slope of the line is. We can do that using this equation:


`m = (y_2 - y_1)/(x_2 - x_1)`

If you are subtracting a negative, flip the sign into a positive. This is because a negative times a negative equals a positive.


`m= (-4 + 20)/(12 - 6); m = (16)/(6)`

Now, we can put
`m` into the slope-intercept form, which is this equation:


`y = mx + b`

Let's input m.


`y=16/6x+b`

After that, we can select any point for the
`x` and
`y` values, input those, and solve for
`b`. 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:


`y = 16/6x - 36`

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).