PROPORTIONAL NONPROPORTIONAL SITUATIONS LESSON 4 4 MAKE A

PROPORTIONAL & NONPROPORTIONAL SITUATIONS LESSON 4. 4

MAKE A T-CHART FOR PROPORTIONAL VS. NON PROPORTIONAL Proportional Non Proportional

EXAMPLE #1: DISTINGUISH BETWEEN PROPORTIONAL AND NON-PROPORTIONAL SITUATIONS USING A GRAPH • Is the graph proportional or non-proportional? • Explain • How could you find the slope and y-intercept of this graph? • Step 1: Plot points on the line • Step 2: Find the slope (two ordered pairs) • Step 3: What is the y-intercept (if x is zero, what is y) • Step 4: What is the equation of the line (y = mx + b) What do the slope and the y-intercept of the graph represent in this situation?

PROPORTIONAL VS NON-PROPORTIONAL USING A TABLE/GRAPH • What does linear mean? • When you evaluate a table, how do you know if it is proportional or non-proportional? • Look to see if there is a constant slope (using slope formula) • If there is a constant, the table is proportional. • When you evaluate a graph, how do you know if it is proportional or nonproportional? • If the line goes through the origin, it is proportional. If the line does not go through the origin, it is non-proportional.

DISTINGUISH BETWEEN PROPORTIONAL/NONPROPORTIONAL SITUATIONS USING A GRAPH PG. 113 Determine if each of the following graphs represents a proportional or non-proportional relationship. Non-proportional Proportional

EXAMPLE #3: DISTINGUISH BETWEEN PROPORTIONAL/NONPROPORTIONAL SITUATIONS USING A TABLE • The values in the table represent the number of U. S. dollars three tourists traded for Mexican pesos. The relationship is linear. Is the relationship proportional or non-proportional? U. S. DOLLARS TRADED • Find the slope. 130 255 505 MEXICAN PESOS RECEIVED 1, 690 3, 315 6, 565 • Are the slopes in the table constant? • Is this table proportional or non-proportional? (Please explain reasoning).

ADDITIONAL EXAMPLE Time (min) 25 45 65 Distance (mi) 15 30 45 • The table shows the distance of a train from a station and the time it will take to arrive. Is it proportional or non-proportional? • Find the slope. • Are the slopes in the table constant? • Is this table proportional or non-proportional? (Please explain reasoning). Pg. 115, Do #9 and #10

DISTINGUISH BETWEEN PROPORTIONAL/NONPROPORTIONAL SITUATIONS USING AN EQUATION •

DISTINGUISH BETWEEN PROPORTIONAL/NONPROPORTIONAL SITUATIONS USING AN EQUATION Determine if each of the following equations represents a proportional or nonproportional relationship. 1. d = 65 t 2. p = 0. 1 s + 2000 3. n = 450 – 3 p 4. 36 = 12 d 1. proportional 2. Non-proportional 3. Non-proportional 4. nonproportional

CARD SORT ACTIVITY • Each group will be given graphs, charts, and equations and a piece of paper that has proportional and non-proportional on it. • Your group will determine if they are proportional or nonproportional. • Your work will go on the back of the papers you are given. • Once you have placed each item under the correct word, your group will get it checked by a teacher.

HOMEWORK • Pg. 117 -199 #1 -6, 8 -9

EXAMPLE #4: COMPARING PROPORTIONAL AND NONPROPORTIONAL SITUATIONS A laser tag league has a choice of two arenas for a tournament. In both cases, x is the number of hours and y is the total charge. Compare and contrast these two situations. • What is the slope for Arena A? • What is the y-intercept for Arena A? • What is the slope for Arena B? • What is the y-intercept for Arena B? • Compare and contrast the slope and y-intercept.

JESSIKA IS REMODELING AND HAS THE CHOICE OF TWO PAINTERS. IN BOTH CASES, X IS THE NUMBER OF HOURS AND Y IS THE TOTAL CHARGE. COMPARE AND CONTRAST THESE TWO SITUATIONS . • What is the slope for Painter A? • What is the y-intercept for Painter A? • What is the slope for Painter B? • What is the y-intercept for Painter B? • Compare and Contrast the Slope and y-intercept.

ADDITIONAL EXAMPLE • The bowling club has a choice between two bowling alleys. In both cases, x is the number of games and y is the total charge in dollars. Compare and contrast these two situations. • Nite Owl Lanes: y = 3. 75 x + 2 • Lucky Five Lanes: X 0 1 3 4 Y 0 4. 5 9 13. 5 Do Pg. 117 #11

HOMEWORK • Pg. 119 -120 #12, 14 -15 • Quiz 4. 4 tomorrow