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Transcript
4.4 – Matching Equations and Graphs Math 9 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 y y y 25 12 12 Monica Sari Bruce 5 2 2 1 m 2d 3 5 x x x 1 5 m 4d 1 m d 5 Describe, in words, each person’s sponsorship plans. 5 Example 1: The 3 graphs on your handout have these equations, but the graphs are not in order. Match each equation with its graph. y 3x 3 xy 3 y 3x 3 Let’s get the equations to all follow the same format. (y=) What is the same about these equations, what is different? What else do you need to determine what a graph looks like? Let’s complete a table of values for each equation. y = 3x + 3 x 0 1 2 y y=3–x x 0 1 2 y y = 3x – 3 x y 0 1 2 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. y = 3x – 3 y = 3x + 3 y=3–x Is there any way you can use the equation to determine what the graph looks like? Match each graph on the grid with the equation... y y=x 8 y = 2x y = -3x x -8 8 We can match the equation to the graph by looking at the coefficient of x. -8 Match each graph on the grid with the equation cont… y=x What is the coefficient for each of these equations? y = 2x y = -3x 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. y = -3x y y=x 8 y = 2x x -8 8 -8 Note… The coefficient of the x term, when written as above, is more commonly referred to as the slope of the equation. Identifying a Graph Given its Equation y 6 Which graph on this grid has the equation y = 3x – 4? Justify your answer. x -4 4 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. -6 Assignment Time Pg. 188-190 #3-9, 11c, 13