Investigating Families of Linear Graphs

Transcription

1 Investigating Families of Linear Graphs Algebra 1 1 day TI-84 Plus Graphing Calculator Carrie Susabach 1

2 Objectives Students will be able to describe the similarities and differences among linear graphs. They will also be able to write a description of the family. NYS Process Strands Problem Solving Strand o A.PS.2 Recognize and understand equivalent representations of a problem situation or a mathematical concept o A.PS.3 Observe and explain patterns to formulate generalizations and conjectures Reasoning and Proof Strand o A.RP.2 Use mathematical strategies to reach a conclusion and provide supportive arguments for a conjecture Communication Strand o A.CM.1 Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem Connections Strand o A.CN.1 Understand and make connections among multiple representations of the same mathematical idea NYS Content Strands Geometry Strand o A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph Materials Class set of TI-84 Plus graphing calculators Overhead projector and attachment for TI-84 Plus graphing calculator Handout Opening Activity Review with students how to reset the memory on the calculators. Ask students to recall how to enter lines into the calculator so we can graph them. Main Activity Give students the handout on Families of Linear Graphs. Discuss what it means to be a family of graphs. 2

3 Ask students to work through Example 1. Pull the class together to write a description of the family and discuss students responses to the other two questions. Repeat the above step with Example 2. Have students try the problems on the back on their own. Closure Have students write a paragraph explaining how the values of m and b in the slope-intercept form affect the graph of a linear equation. 3

4 Name Date Period Families of Linear Graphs What is a family? What is a family of linear graphs? Example 1 Graph y = x, y = x + 4, and y = x 2 in the standard viewing window. Example 2 Graph y = x +1, y = 2x + 1, and y = -1/3x + 1 in the standard viewing window. 4

5 Extra Practice Graph each set of equations on the same screen. Describe any similarities or differences among the graphs. If the graphs are part of a family, describe the family. 1. y = -4 y = 0 y = 7 2. y = -x + 1 y = 2x + 1 y = 1/4x y = x + 4 y = 2x + 4 y = 2x 4 4. y = -2x - 2 y = 2x 2 y = 1/2x 2 5. y = 3x y = 3x + 6 y = 3x 7 5

6 Name Answer Key Date Period Families of Linear Graphs What is a family? A family of people is a group of people related by birth, marriage, or adoption. What is a family of linear graphs? Graphs and equations of graphs that have at least one characteristic in common. They fall into two categories those with the same slope and those with the same y-intercept. Example 1 Graph y = x, y = x + 4, and y = x 2 in the standard viewing window. They have the same slope. They are parallel. They have different y-intercepts. Linear graphs with a slope of 1. Example 2 Graph y = x +1, y = 2x + 1, and y = -1/3x + 1 in the standard viewing window. They have the same y-intercept. They have different slopes. Linear graphs with a y-intercept of 1. 6

7 Extra Practice Graph each set of equations on the same screen. Describe any similarities or differences among the graphs. If the graphs are part of a family, describe the family. 1. y = -4 y = 0 y = 7 They have the same slope but different y-intercepts. They are all horizontal lines. The family can be described as linear graphs with a slope of y = -x + 1 y = 2x + 1 y = 1/4x + 1 They have different slopes but the same y-intercepts. Linear graphs with a y-intercept of y = x + 4 y = 2x + 4 y = 2x 4 All 3 of them have nothing in common. 4. y = -2x - 2 y = 2x 2 y = 1/2x 2 They have different slopes but the same y-intercept. Linear graphs with a y-intercept of y = 3x y = 3x + 6 y = 3x - 7 They have the same slope but different y-intercepts. Linear graphs with a slope of 3. 7