Proportional & Non-proportional Situations Lesson 4.4

Make a t-Chart for Proportional Vs. 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 non- proportional? 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/non-proportional situations using a graph Pg. 113 Determine if each of the following graphs represents a proportional or non-proportional relationship. Non-proportional Proportional

MEXICAN PESOS RECEIVED Example #3: distinguish between proportional/non-proportional 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? Find the slope. Are the slopes in the table constant? Is this table proportional or non-proportional? (Please explain reasoning). U.S. DOLLARS TRADED MEXICAN PESOS RECEIVED 130 1,690 255 3,315 505 6,565

Additional Example Time (min) 25 45 65 Distance (mi) 15 30 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 Time (min) 25 45 65 Distance (mi) 15 30

distinguish between proportional/non-proportional situations using an equation A linear equation of the form y = mx + b may represent either a proportional or non-proportional relationship. If b = 0, it is proportional. If b ≠ 0, it is non proportional. The number of years since Keith graduated from middle school can be represented by the equation y = a – 14, where y is the number of years and a is his age. Is the relationship between the number of years since Keith graduated and his age proportional or non- proportional?

distinguish between proportional/non-proportional situations using an equation Determine if each of the following equations represents a proportional or non- proportional relationship. 1. d = 65t 2. p = 0.1s + 2000 3. n = 450 – 3p 4. 36 = 12d 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 non- proportional. 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 non-proportional 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 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 = 3.75x + 2 Lucky Five Lanes: X 1 3 4 Y 4.5 9 13.5 Do Pg. 117 #11

Homework Pg. 119-120 #12, 14-15 Quiz 4.4 tomorrow