Equations and Graphs

Contributor: Marlene Vogel. Lesson ID: 10901

Have you ever gotten a "bee" in algebra? Does math give you hives? Watch a simple video, use an online grapher, and learn to write and solve your own equations in tables and turn them into bar graphs!


Functions, Pre-Algebra

learning style
personality style
Otter, Golden Retriever
Grade Level
Middle School (6-8)
Lesson Type
Dig Deeper

Lesson Plan - Get It!


Vocabulary (All definitions can be found at A Maths Dictionary For Kids Quick Reference by clicking on the terms):

This lesson focuses on how to take an equation, and data computed from that equation, and create a graph.

Consider the following math problem:

Lee paints race cars. Lee receives $160 for each race car he paints. How much money will Lee receive if he paints 3 race cars, 6 race cars, and 10 race cars? Develop a graph to represent the data from this problem.

  1. Your first step is to understand the problem. You can see that each time Lee paints a race car, he is paid $160. The problem wants you to figure out how much money Lee will receive if he paints 3, 6, and 10 race cars.
  2. The next step is to write an equation representing the problem. Let the variable y represent the amount of money Lee receives after painting the race cars. Let x represent the number of race cars Lee paints. Your equation would look like the following:
    y = 160x
    1. Remember, the number 160 in the equation represents the amount of money per car Lee receives when he is finished painting one car.
  3. Step three is to set up a table. This table will help you figure out the data for the problem. See the table below:
    x y = 160x y

    1. Remember, the variable x represents the number of race cars Lee paints. You know how much he gets paid if he paints 1 race car, so you should include the number 1 in the x column. Include the number 2 just to make sure you understand how to compute the answer for y. The rest of the numbers you should place in the x column should come from the original problem (3, 6, 10). See below for the completed portion of the table:
      x y = 160x y
  4. The middle column is where you are going to do your calculations. For example, for the quantity of 1, the equation in the middle column should look like y = 160(1). The number "one" in the parentheses represents the quantity of race cars Lee has painted, which in this case is one. See the table below with this information filled in:
    x y = 160x y
    1 y = 160(1)  
  5. To find the value of y, multiply 160 and 1. The value of y is 160. See below with this information filled in:
    x y = 160x y
    1 y = 160(1) 160
  6. Calculate the value for y for the remaining x values using the same process (A completed table and the answers for the problem are located at the end of this section of the lesson.).
  7. Answer the questions from the problem, "How much money will Lee receive if he paints 3 race cars, 6 race cars, and 10 race cars?"
  8. The last step of this problem is to develop a graph representing the data you computed in the table. You will develop a bar graph.
  9. Before constructing your bar graph, watch the following How-to...Draw a Bar Graph video:

  10. Below are the steps you will need to take when making your own bar graph for the problem. You may find it easier to draw your graph on a piece of graph paper.
    1. Draw your x- and y- axes. Remember, your x-axis values will be the number of race cars Lee paints, and your y-axis values will be the amount of money Lee receives as payment (See below):
      graph for 10a
    2. Label your x- and y-axes (See below):
      graph for 10b
    3. Now it is time to graph your data. Look at the table you made above. You know that if Lee paints 1 race car, he receives a payment of $160. On your graph, you are going to draw a rectangle that begins above the number one on the x-axis and ends at 160 on the y-axis. In the example above, you will not see the number 160 on the y-axis, so you will have to estimate where your rectangle or bar ends (See below):
      graph for 10c
    4. Complete putting the rest of the data into your graph (See below):
      graph for 10d

Congratulations! You have just completed making your first graph that relates to an equation!

Check your answers to see how you did.

Now, go back to the activity at the beginning of the lesson (Honey Production) and complete it.

The Got It? section offers you opportunities to practice the skill of creating a graph that relates to an equation.

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