# How do you write an equation of the line given (2,4)and (6,-2)?

Mar 14, 2018

$y = - \frac{3}{2} x + 7$

#### Explanation:

To find an equation of a line, when given two points, we first must find the slope.

We can find the slope, using this expression:

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Knowing this, we plug in our values for each:

$\frac{- 2 - 4}{6 - 2}$

$- \frac{6}{4}$

$- \frac{3}{2}$

Now that we know our slope, we can use that and any one of the points to find our equation.

To find our equation with the information given, we need to use point-slope form:

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

We can now plug our values in:

$y - 4 = \left(- \frac{3}{2}\right) \left(x - 2\right)$

$y - 4 = - \frac{3}{2} x + 3$

$y = - \frac{3}{2} x + 7$