# How do you write the equation of the line with a slope of 2/3 and passing through the point (6,-2)?

Aug 30, 2016

We begin by writing $y = \frac{2}{3} x + b$

#### Explanation:

Now plug in the values for $x$ and $y$ from the point $\left(6 , - 2\right)$

$- 2 = \frac{2}{3} \cdot 6 + b \to - 2 = 4 + b \to b = - 6$

So the equation in slope-intercept form is:
$y = \frac{2}{3} x - 6$
graph{2/3x-6 [-5.25, 14.75, -7.44, 2.56]}

Aug 30, 2016

$y = \frac{2}{3} x - 6$

#### Explanation:

If we are given the slope and one point, substitute these values into the following formula which is based on the definition for slope.

$y - {y}_{1} = m \left(x - {x}_{1}\right) \textcolor{w h i t e}{\times \times} \leftarrow m = \frac{2}{3} \mathmr{and} \left(6 , - 2\right)$

$y - \left(- 2\right) = \frac{2}{3} \left(x - 6\right) \textcolor{w h i t e}{\times \times} \leftarrow$ multiply out and simplify.

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

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

$y = \frac{2}{3} x - 6$