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# 2022 PA-A-2-4

last edited by 10 months ago

PA.A.2.4

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 a change in the slope of a line affects the steepness of the line. Specifically, students should understand as the slope is changed to be a value closer to zero, the line rotates to become more horizontal and a line becomes more vertical as the slope changes to a  value farther from zero. 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. Students should notice and understand that when the y-intercept value increases, the line will shift vertically in the positive direction. Alternatively, when the y-intercept value decreases, the line will shift vertically in the negative direction.

## Teacher Actions

• Develop Ability to Make Conjectures, Model and Generalize when exploring patterns in behaviors of slope and y-intercepts of various linear functions, including the use of graphing technology, to develop general conclusions and make predictions about how the graph of a linear function is affected by changes to these properties.

• Develop Ability to Communicate Mathematically when transferring understanding of slope properties with linear functions to mathematically justifying a slope relationship between points on a line, including the y-intercept, and changes to the value of slope with both written and verbal descriptions.

• 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 that support student discovery of how slope and y-intercept properties affect graphs of linear functions.

• Implement meaningful tasks that promote reasoning and problem solving through the discovery of properties, including the use of technology, resulting from changes to linear function on their graphs, table of points, and equations.

• Use and connect mathematical representations by providing opportunities for students to develop and examine models of linear functions involving variations of slope and y-intercept properties. Include multiple examples of both changes to slope (positive, negative, less than 1, equal to 1, and greater than 1) and the y-intercept (positive and negative).

## Misconceptions

• Describe the effects of a graph when the slope (rate of change) of a line is changed.

• The steepness of the line decreases and approaches a horizontal line when its value becomes closer to zero.

• The steepness of the line increases and approaches a vertical line when its value becomes farther from zero.

• When changing a slope value’s sign, it will change the direction of the line.  For example, if a slope is changed from 2 to -2, the line will change from an increasing line to a decreasing line.

• Know how changing the y-intercept affects the graph of the linear function.  Changing the y-intercept to a greater value will shift the line up vertically while changing the y-intercept to a lesser value will shift the line down vertically.

• The y-intercept is the only point that remains the same after a change in the value of the slope of a line.

• Students will sometimes mix up the slope and y-intercept, therefore confusing how it affects the line on the graph when either the slope or y-intercept is changed.

• When evaluating a graphed line, students may not correctly recognize the direction and or steepness of a line when given the value of a slope.

• A student may not correctly identify a y-intercept and instead choose a value on the x-axis, usually confusing it with the x-intercept.

## Prior Knowledge

• Identify graphical properties of linear functions, including slope and intercepts (PA.A.2.3).
• Recognize the parent functions f(x)=x and f(x)=x. Predict the effects of vertical and horizontal transformations f(x+c) and f(x)+c, algebraically and graphically (A1.F.2.2).

• Identify the parent forms of exponential, radical, quadratic, and logarithmic functions.  Predict the effects of transformations algebraically and graphically (A2.F.1.2).

OKMath Framework Introduction

Pre-Algebra Introduction