Carrie Johnston
Algebra I Lesson Plans 11/15-12/13/2012
Unit 4A Investigating Linear Functions
Lesson Synopsis: Students identify the linear parent function and describe the effects of parameter
changes on the graph of the linear parent function. Characteristics of linear functions, including slope,
intercepts, and forms of equations, are investigated. Linear functions are written and evaluated in function
notation. Two-variable linear inequalities are represented graphically.
Key Understandings:
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The linear parent function is y = x. Linear functions can be proportional (direct variation, y = kx) where
y = mx or non-proportional where y = mx + b, b ≠ 0.
Linear functions can be represented using tables, graphs, and algebraic generalizations, and
connections can be used to translate between representations.
Slope (constant rate of change), x-intercepts, and y-intercepts can be found from a table, graph, or
algebraic generalization and have specific meanings in mathematical and real-world situations.
Changes in the slope and y-intercept have specific effects on the graph of the representative function
and in the problem situation.
Problem situations can be modeled using two-variable inequalities, and the solution can be
represented graphically on a coordinate plane.
Unit Activities:
1. Meet Your Parent (WS)
Students use prior knowledge to make a scatterplot of data points that define
the linear parent function and analyze the results.
2. What’s Up with “m” (overhead) Students use the graphing calculator and describe changes to the linear
3. What’s Up with “b” (overhead) parent function caused by changing the parameters of m and b. Students
generalize the effects of those parameter changes on the linear parent
function.
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Parameter Changes on the Linear Parent Function (WS)
Investigating Slope (WS)
Finding Slope from a Graph (WS) Homework
Finding Slope from Two Points (WS) Homework
Finding Slope from an Equation (WS) Homework
9. Investigating Intercepts (WS)
10. Activity
11. Review
12. Test
Students define slope as a rate of change
and determine slope from graphs, tables,
and algebraic representations.
Students determine y-intercepts and x-intercepts from various
representations.
Students collect and analyze real world data on concepts of slope
and intercept. Students determine a trend.
line by adjusting the parameters of m and b on y = mx + b.
Vocabulary: constant of proportionality, direct variation, increasing, decreasing, rate of change,
slope, independent, dependent, vertical change, horizontal change, linear function, linear inequality,
x-intercept, y-intercept, function notation, parent function, zero of a function, domain, range,
parameter change