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Proportional & Non-proportional Situations
Lesson 4.4
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Make a t-Chart for Proportional Vs. Non proportional
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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?
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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.
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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
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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
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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
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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?
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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 n = 450 – 3p = 12d 1. proportional 2. Non-proportional 3. Non-proportional 4. nonproportional
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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.
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Homework Pg #1-6, 8-9
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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.
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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.
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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
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Homework Pg #12, 14-15 Quiz 4.4 tomorrow
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