## Real World Applications – Algebra I

### Topic

Where do we see parallel and perpendicular lines in every day life?

### Student Exploration

Things you might need: graph paper, ruler, markers

You will need a printer to print pictures, or you might need some expert Photoshop skills for this activity!

You’ll first need to look around your neighborhood and find examples of parallel and perpendicular lines. Once you get pictures, you will then create equations for all of these lines you’ve found. Let’s do one of these together, then you try on your own.

I found the following picture of a car grille. Do you think this represents a set of parallel or perpendicular lines?

This image shows sets of parallel lines. I’m going to add a set of

To find the equation of the first line (let’s say it’s the leftmost line drawn in turquoise below), we need to calculate the slope and find the

Let’s calculate the slope first. I’m going to find two different points on this line and find the difference between the

For the turquoise line, it looks like the slope is

We will also do the same for the purple line. The

Now, we should notice that parallel lines have the same slope, and different

What are other equations that you can see on the car grille? This car grille represents one family of functions, where the slopes of all of the lines are the same.

Now, let’s take a look at this picture below of kitchen tiles.

I took a piece of this picture and added some axes and perpendicular lines.

Let’s find the equations of these lines and verify that these are perpendicular lines.

First, let’s look at the turquoise line. It looks like the

For the purple line, the

Looking at the two equations, we can tell that this represents a pair of perpendicular lines because the slopes are opposite reciprocals of each other. Remember, the

### Extension Investigation

Try finding a picture online and print it out, or take a picture and get it developed of both parallel lines and a picture that represents perpendicular lines. Find the equations of these lines, and prove that they are parallel or perpendicular using Algebra!

Also try to find a picture that would represent the second family of functions, where the y-intercept is the same for all of the lines. What are the equations of those lines?

### Resources Cited

Shutterstock images: 48660352, 56409679