# What is the equation of a line that goes through (7, -7) and has a slope of -3?

##### 1 Answer
Nov 19, 2015

You use standard form of $y = m x + c$ and substitute in the given values to find the value of c

$y = \left(- 3\right) x + 14$

#### Explanation:

Using $y = m x + c$ and universal notation of $\left(x , y\right)$

Let $y = - 7$
Let $x = 7$
Let $m = - 3 \textcolor{w h i t e}{\times x}$ (this is fixed. It does not change!)

Giving:

$- 7 = \left(- 3\right) \left(7\right) + c$

$- 7 = - 21 + c$

Add +21 to both sides:

$- 7 + 21 = - 21 + 21 + c$

$14 = 0 + c$

$c = 14$

So the full equation of the line is:

$y = \left(- 3\right) x + 14$