# How do you write the equation of the line parallel to y = 3x - 4 and passing through the point (-2, 5)?

Aug 25, 2016

$y = 3 x + 11$

#### Explanation:

Parallel lines have the same slopes.

The slope of the new line will have the same slope as the given line:

$y = \textcolor{red}{3} x - 4 \Rightarrow m = \textcolor{red}{3}$

One point on the line is given, $\textcolor{b l u e}{\left(\left(- 2 , 5\right)\right)} . \text{This is } \textcolor{b l u e}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$

The formula for slope is $m = \left(\text{change in y values"/"change in x-values}\right) = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.

$y - \textcolor{b l u e}{{y}_{1}} = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$y - \textcolor{b l u e}{5} = \textcolor{red}{3} \left(x - \textcolor{b l u e}{\left(- 2\right)}\right)$
$y - 5 = 3 \left(x + 2\right)$

Simplify to get the required equation of the line.

$y = 3 x + 6 + 5$

$y = 3 x + 11$