## Finding an Equation of a Line Parallel to a Given Line

Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope—just what we need to use the point–slope equation.

First let’s look at this graphically.

The graph shows the graph of \(y=2x-3\). We want to graph a line parallel to this line and passing through the point \(\left(-2,1\right)\).

We know that parallel lines have the same slope. So the second line will have the same slope as\(y=2x-3\). That slope is\({m}_{\parallel }=2\). We’ll use the notation \({m}_{\parallel }\) to represent the slope of a line parallel to a line with slope \(m\). (Notice that the subscript \(\parallel \) looks like two parallel lines.)

The second line will pass through \(\left(-2,1\right)\) and have \(m=2\). To graph the line, we start at\(\left(-2,1\right)\) and count out the rise and run. With \(m=2\) (or \(m=\frac{2}{1}\)), we count out the rise 2 and the run 1. We draw the line.

Do the lines appear parallel? Does the second line pass through \(\left(-2,1\right)\)?

Now, let’s see how to do this algebraically.

We can use either the slope–intercept form or the point–slope form to find an equation of a line. Here we know one point and can find the slope. So we will use the point–slope form.

### Example: How to Find an Equation of a Line Parallel to a Given Line

Find an equation of a line parallel to \(y=2x-3\) that contains the point \(\left(-2,1\right)\). Write the equation in slope–intercept form.

### Solution

Does this equation make sense? What is the *y*-intercept of the line? What is the slope?

### Find an equation of a line parallel to a given line.

- Find the slope of the given line.
- Find the slope of the parallel line.
- Identify the point.
- Substitute the values into the point–slope form, \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
- Write the equation in slope–intercept form.

Ever wandering where to shop for your baby collections online???

Visit http://dachi.co.uk today and shop from dachi baby and mom collections at affordable prices

.

Click the link to get started

Dachi.co.uk