1. 4.4 – Matching Equations and Graphs Math 9

2. 3 students participate in a 5-km walk for charity. Each student has a different plan to raise money from his/her sponsors. These graphs show how the amount of money a sponsor owes related to the distance walked.  Match each graph with its equation  Describe, in words, each person’s sponsorship plans. Sari Monica Bruce

3. Example 1: The 3 graphs on your handout have these equations, but the graphs are not in order. Match each equation with its graph. What is the same about these equations, what is different? Let’s get the equations to all follow the same format. (y=) What else do you need to determine what a graph looks like?

4. y = 3 – x xy 0 1 2 xy 0 1 2 xy 0 1 2 y = 3x + 3 y = 3x – 3 So, to match each equation with its graph, use the equation to determine 3 points. Then find out which graph passes through those 3 points. Let’s complete a table of values for each equation.

5. Is there any way you can use the equation to determine what the graph looks like? y = 3 – x y = 3x + 3 y = 3x – 3

6. Match each graph on the grid with the equation... y = x y = 2x y = -3x We can match the equation to the graph by looking at the coefficient of x.

7. y = x y = 2x y = -3x Match each graph on the grid with the equation cont… What is the coefficient for each of these equations? Remember, for each equation we’ve created before, the coefficient describes what happens to y when the x-value increases by 1.  A coefficient of 1 means that when x increases by 1 unit, y also increases by 1 unit.  A coefficient of 2 means that when x increases by 1 unit, y increases by 2 units.  A coefficient of -3 tells us that y decreases by 3 units when x increases by 1 unit.

8. y = x y = 2x y = -3x Note… The coefficient of the x term, when written as above, is more commonly referred to as the slope of the equation.

9. Identifying a Graph Given its Equation Which graph on this grid has the equation y = 3x – 4 ? Justify your answer. To solve this problem, pick 2 points on each graph and check to see if they satisfy the equation. Remember to evaluate the left side and right side independently.

10. Assignment Time Pg. 188-190 #3-9, 11c, 13