# How do you write the equation of a line passing through the point (4,2) with the slope -3?

Nov 21, 2016

Point-slope form: $y - 2 = - 3 x + 12$

Slope-intercept form: $y = - 3 x + 14$

#### Explanation:

First write a point-slope equation $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $\left({x}_{1} , {y}_{1}\right)$ is the given point, $\left(4 , 2\right)$, and $m$ is the slope, $- 3$.

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

$y - 2 = - 3 x + 12$

For graphing, you can convert to the slope-intercept form, $y = m x + b$, by solving for $y$, where $m$ is the slope and $b$ is the y-intercept.

Add $2$ to both sides.

$y = - 3 x + 12 + 2$

$y = - 3 x + 14$

$m = - 3$ and $b = 14$

graph{y=-3x+14 [-10.72, 9.29, 7.66, 17.66]}