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

Dec 13, 2016

$y - 14 = - \frac{1}{4} \left(x + 8\right) \mathmr{and}$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 $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

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

$m = \frac{17 - 14}{- 20 - - 8}$

$m = \frac{3}{- 20 + 8}$

$m = - \frac{3}{12}$

$m = \left(\frac{3}{3}\right) \times \left(- \frac{1}{4}\right)$

$m = 1 \times \left(- \frac{1}{4}\right)$

$m = - \frac{1}{4}$

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

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

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:

$y - 14 = - \frac{1}{4} \left(x - - 8\right)$

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

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

$y - 14 = - \frac{1}{4} x + - \frac{1}{4} \times 8$

$y - 14 = - \frac{1}{4} x - \frac{8}{4}$

$y - 14 = - \frac{1}{4} x - 2$

$y - 14 + 14 = - \frac{1}{4} x - 2 + 14$

$y - 0 = - \frac{1}{4} x + 12$

$y = - \frac{1}{4} x + 12$