Question

What is the equation of the line that goes through `(- 19- 6)` and `( 15,16)`?

Answer 1

`y = 11/17x + 107/17`

Explanation:

graph{y = (11/17)x + (107/17) [-25.6, 25.71, -12.84, 12.8]}

This is simply an exercise of the point-slope form of a line

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

The different `x` and `y` values correspond to their appearance in those two points.

The slope, `m`, in this case, becomes

`m = (16 - (-6))/(15 - (-19)) = 22/34 = 11/17`

Now that you have the slope, you need a `y`-intercept for your equation to be complete.

To find this, just plug the `x` and `y` values from either point into your incomplete equation

`y = (11/17)x + b`

to solve for `b`.

In this case, this `b` value is

`16 = 11/17 * 15 + b`

`b = 107/17`

Thus your completed equation should be

`y = 11/17x + 107/17`