# How do you determine the equation of the line given A(-6, -2), B(6, 8)?

Oct 18, 2017

$y = \frac{5}{6} x + 3$

#### Explanation:

The first step would be to find the slope that would be used in the equation. This is done using the slope formula, $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. So,
$\frac{8 - \left(- 2\right)}{6 - \left(- 6\right)}$ = $\frac{10}{12}$ = $\frac{5}{6}$

Therefore the slope would be 5/6. Now we take this slope and one of the points given to us and we plug them into the equation of a line, $y = m x + b$. Let's use point B, (6,8)

$8 = \frac{5}{6} \left(6\right) + b$
$8 = 5 + b$
$b = 3$

Then we plug the m and b values we have found into $y = m x + b$ to create the equation of the line.
$y = \frac{5}{6} x + 3$