# What is the equation of the line that passes through the point (5,9) and is parallel to the line y = 3x + 7?

Jul 1, 2015

I found:
$y = 3 x - 6$

#### Explanation:

You can use the relationship:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
Where:
$m$ is the slope
${x}_{0} , {y}_{0}$ are the coordinates of your point:
In your case the slope of the parallel line must be the same as the one of your given line which is: $m = 3$ (the coefficient of $x$).
So you get:
$y - 9 = 3 \left(x - 5\right)$
$y = 3 x - 15 + 9$
$y = 3 x - 6$

Graphically:

(red line is the parallel)