# How do you write an equation of a line given slope -3 and passes through (5,2)?

Mar 3, 2017

$y = - 3 x + 17$

#### Explanation:

The general formula for a line is $y = m x + c$ where $m =$ gradient and $c =$ the $y$ intercept.

Using the numbers you have been given in the question, you can put these numbers into the general formula to calculate $c$.

From the coordinates given, the $x$ is 5 and $y$ is 2.
$2 = - 3 \cdot 5 + c$
$2 = - 15 + c$
$c = 17$
Now you have worked out the value of $c$, (the $y$ intercept), you can give the equation of the line, by inserting $- 3$ in place of the $m$ and $17$ in place of the $c$:
$y = - 3 x + 17$