# How do you write an equation of a line that passes through the point (3, 2) and is parallel to the line y=3x-4?

Dec 16, 2016

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

#### Explanation:

For a line to be parallel to another line, by definition it must have the same slope. Because the equation is in the slope-intercept form we can use the slope of the line.

The slope-intercept form of a linear equation is:

$\textcolor{red}{y = m x + b}$
Where $m$ is the slope and $b$ is the y-intercept value.

Therefore, for the given equation the slope is $3$.

Now we can use the point slope formula to determine the equation for the parallel line.

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $m$ is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope from the given line and the given point gives:

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

Transforming this to the slope-intercept form by solving for $y$ gives:

$y - 2 = 3 x - 9$

$y - 2 + 2 = 3 x - 9 + 2$

$y = 3 x - 7$