# What is the equation of the line that is parallel to y = 2x + 3 and passes through (-3,4)?

Apr 8, 2015
• Parallel Lines have the SAME SLOPE

• We first Find the Slope of the line $y = 2 x + 3$
The Slope Intercept Form of the equation of a given line is:
$y = m x + c$
where $m$ is the Slope of that line, and $c$ is the Y intercept.
For this line, the Slope is $\textcolor{g r e e n}{2}$

• So the Slope of the line PARALLEL to $y = 2 x + 3$ will also be $\textcolor{g r e e n}{2}$. And we are given that it passes through the point $\left(- 3 , 4\right)$
With this, we can use the Point Slope form to find the equation of the line.

The Point-Slope form of the Equation of a Straight Line is:
$\left(y - k\right) = m \cdot \left(x - h\right)$
$m$ is the Slope of the Line

$\left(h , k\right)$ are the co-ordinates of any point on that Line.

Here, we have been given the coordinates $\left(h , k\right)$ of 1 point on that line as $\left(- 3 , 4\right)$
And the Slope $m$ is $\textcolor{g r e e n}{2}$

Substituting the values of $h , k \mathmr{and} m$ in the Point-Slope form, we get

$\left(y - 4\right) = \left(2\right) \cdot \left(x - \left(- 3\right)\right)$
The above will be the Equation of the Line in Point-Slope form.

• If we need it in the Slope Intercept Form, we need to follow these steps:

Modifying the equation, we get:

$\left(y - 4\right) = 2 \cdot \left(x + 3\right)$

$y - 4 = 2 x + 6$

$y = 2 x + 6 + 4$

We get the equation of the line as :
color(blue)( y=2x+10

• The graph will look like this:

graph{y=2x+10 [-10, 10, -5, 5]}