# What is the equation of a line that passes through (2, —7), and has a slope of 3?

Apr 24, 2018

$y = 3 x - 13$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where x is the slope and b the y-intercept}$

$\text{here } m = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(2,-7)" into the partial equation}$

$- 7 = 6 + b \Rightarrow b = - 7 - 6 = - 13$

$\Rightarrow y = 3 x - 13 \leftarrow \textcolor{red}{\text{is the equation of line}}$

Apr 24, 2018

$\textcolor{\in \mathrm{di} g o}{3 x - y = 13}$

#### Explanation:

Point: $\left({x}_{1} , {y}_{1}\right) = \left(2 , - 7\right)$

Slope $= m = 3$

The point - slope form equation is

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

So

$y + 7 = 3 \cdot \left(x - 2\right)$

$y + 7 = 3 x - 6$

$\textcolor{\in \mathrm{di} g o}{3 x - y = 7 + 6 = 13}$