Proportional and Non-Proportional Relationships

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Presentation transcript:

Proportional and Non-Proportional Relationships Lesson 4.4

Proportional vs Nonproportinoal What does linear mean? It forms a line. When you evaluate a table, how do you know if it is proportional or non-proportional? See if there is a constant slope. Formula: 𝑦 𝑥 or 𝑦 2 - 𝑦 1 𝑥 2 - 𝑥 1 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? Does the line go through the origin….if it does it is proportional. If the line does not go through the origin, it is not proportional.

Example #1: Look at Example #1 on page 113. Please draw out the graph on your notes. Is the graph proportional or nonproportional and explain your reasoning in a complete sentence. How could you find the slope and y-intercept of this graph? First step: plot points on the line. Second step: Find the slope y₂ - y ₁ x₂ - x ₁ Third step: find the y-intercept If x is zero what is the y-coordinate. That will be your y-intercept. Forth step: What is the equation of the line y=mx+b

Complete “Your Turn” #1 and #2 on page 113 for practice. Identify if the graph represents a proportional or nonproportional relationship and explain why… Find the slope and y-intercept of each line. Write an equation for each graph. Answer #1: The graph is nonproportional because the line does not go through the origin. Slope: 1 Y-Intercept: 1 Equation: y=1x+1 Answer #2: The graph is proportional because the line goes through the origin. Slope: ¼ Y-Intercept: 0 Equation: y=1/4x+0 or y=1/4x

Mexican Pesos Received Example#3: The values in the table represent the numbers of U.S. dollars three tourists traded for Mexican pesos. The relationship is linear. Is the relationship proportional or non-proportional Find the slope using ordered pairs. Are the slopes in the table constant? Is this table proportional or non-proportional (Please explain your reasoning). U.S. Dollars Traded (X Value) Mexican Pesos Received (Y Value) 130 1,690 255 3,315 505 6,565

Directions for “Your Turn” Please complete “Your Turn” #9 and 10 on page 115. Please give an explanation on why the table is proportional or non-proportional.

Example #4: Read Example #4 on page 116. Read Part B to example #4 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? Read Part B to example #4 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? Complete “Your Turn” on page 117 #11.