Question

How do you write the equation of a line with points (-8,14), (-20,17)?

Answer 1

`y - 14 = -1/4(x + 8) or`y = -1/4x + 12#

Explanation:

To find the equation for these two points we must first determine the slope of the line.

The slope can be found by using the formula:

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

Where `m` is the slope and `(x_1, y_1)` and `(x_2, y_2)` are the two points.

Substituting the points we are give allows us to calculate the slope as:

`m = (17 - 14)/(-20 - -8)`

`m = 3/(-20 + 8)`

`m = -3/12`

`m = (3/3) xx (-1/4)`

`m = 1 xx (-1/4)`

`m = -1/4`

Now, we can use the point-slope formula to find the equation for the line. The point-slope formula states:

`(y - y_1) = m(x - x_1)`

Where `m` is the slope and #(x_1, y_1) is a point the line passes through.

We can substitute the slope we calculated earlier and one of the points to obtain our equation for the line:

`y - 14 = -1/4(x - -8)`

#y - 14 = -1/4(x + 8)

Or solving for `y` to put the equation into slope intercept form gives:

`y - 14 = -1/4x + -1/4 xx 8`

`y - 14 = -1/4 x - 8/4`

`y - 14 = -1/4x - 2`

`y - 14 + 14 = -1/4x - 2 + 14`

`y - 0 = -1/4x + 12`

`y = -1/4x + 12`