Lesson Plan - Get It!
In Romeo and Juliet, William Shakespeare wrote this famous line about a rose by any name smelling just as sweet.
- Did you know that not all roses actually smell sweetly in real life?
It's true! Some have no scent at all.
Okay, so we want to smell the roses before we buy them to make sure they smell sweetly.
- Is there anything else we want to know before we buy them?
We would want to know how much they cost.
- Are roses cheaper at one place than they are at another?
- Is there a way I can use math to help me figure this out?
The answer is, simply, yes! And we are going to do it with graphing, which so many people love!
Let's look at this scenario:
Kathy's Florist sells vases with roses for a setup fee of $5, plus $3 per each rose. Save-a-Lot Florist sells their vases with roses for a setup fee of $8, plus $2 per rose.
- At which number of roses will both florists have the same price?
Here's how we set it up:
Let x represent the roses.
setup fee of $5, plus $3 per each rose
Equation: y = 3x + 5 ($3 per rose, plus $5 setup fee)
setup fee of $8, plus $2 per each rose
Equation: y = 2x + 8 ($2 per rose, plus $8 setup fee)
Since there are two equations, this is called a system of equations.
We can solve this system in a variety of ways.
One way is to make a table, graph the equations, and look at their intersection. We will start off with graphing Kathy's Florist equation y = 3x + 5:
Substitute the numbers 0, 1, 2, 3, 4, and 5 in the place of x and solve for y.
Once you have done that, you will have the values for y and the points that will need to be graphed:
Now, let's graph Save-a-Lot's equation y = 2x + 8.
We will graph it the same way as Kathy's Florist graph. Set up a table, substitute the numbers for x, and then graph. Here is that data:
To determine the number of roses bought where both florists have the same price, we can graph both lines on the same coordinate plane:
- Did you notice that there is an (x, y) coordinate that matches on both tables?
- And that this point is where the two lines intersect?
Look at (3, 14).
This coincides with (number of roses, total cost). So for 3 roses, it costs $14 at both florists.
Now that you have a handle on solving systems by graphing, let's move on to the Got It? section.