If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

PA-A-2-4

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.A.2.4 Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects.

In a Nutshell

Given a linear relationship, students should be able to state that if you change the slope of a line to be a value closer to zero, the line rotates to become more horizontal. Also, students should be able to describe the change in the slope of a line to become more vertical as you change the slope value to a number farther from zero. These changes can be observed by using the same domain to create multiple data tables, or by analyzing the change in y values on different lines. Students should also work and analyze the effects of changing the sign of the slope (negative to positive, positive to negative) and understand that this will cause the line to change to either an increasing or decreasing line. Focus should also be given to the effects of changing the y-intercept. Students should notice and understand that when the y-intercept value increases, the line will shift up. When the y-intercept value decreases, the line will shift down.

Student Actions	Teacher Actions
Develop Ability to Make Conjectures, Model and Generalize by using graphing technologies to explore the effect of making changes to the slope or y-intercept on the graph and to the linear equation. Develop Ability to Make Conjectures, Model and Generalize by predicting what part of the equation changes when a change is made to the slope or y-intercept of a linear function. Develop Ability to Communicate Mathematically when a change is made to a linear function’s slope; justify mathematically, with a table, and on a graph why the y-intercept is the only point that remains the same after changing the slope. Discuss with a partner your reasoning for why the other points are no longer on the line. Develop Mathematical Reasoning by identifying when a change is made to the y-intercept of a linear function and justifying the change mathematically, with a table, and on a graph. Also, explain why none of the original line’s points are on the new line.	Pose purposeful questions such as: What happens to the graph when m is made greater? What happen to the graph when m is made smaller? What happens when m is negative? What happens when m is zero or undefined? What happens with b is made greater or smaller? Implement meaningful tasks that promote reasoning and problem solving by using technological exploration of changes to linear function on their graphs, table of points, and equations. Implement meaningful tasks that promote reasoning and problem solving by requiring students to explain and justify what happens when a linear function is changed. Use multiple examples of both changes to slope (positive/negative and large/small) and y-intercept (positive/negative and large/small).
Key Understandings	Misconceptions
Describe what happens to a graph when the unit rate (coefficient, slope) is changed; Know how changing the y-intercept effects the line on the the graph.	Students will sometimes mix up the slope and y-intercept, therefore confuse how it affects the line on the graph when either the slope or y-intercept is changed. When evaluating a graphed line students may confuse the direction of the line so when the slope changes they may not understand how it effects the sign of the slope.