Lesson 1: Linear Functions
Duration of Days: 2
Lesson Objective
Find the slope of a line given two points.
Understand that linear functions are lines which have constant slope and that positive and negative slope indicate if the functions is increasing or decreasing
What do we need to know in order to determine if a function is linear? The slope must be?
What is the ratio to find rate of change and slope?
What can a linear graph tell you about the relationship that it represents?
Slope
Slope-intercept form
Line
Linear
F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Lesson Description
This lesson focuses on the properties that make a function linear. Students will learn to recognize linear relationships across different formats by: Graphing via Slope and Intercept: Using the "rise over run" method to plot a line starting from the y-intercept, which is more efficient than the point-plotting method.
Purpose: The purpose of Section 9.1 is to establish a standardized model for growth. Most foundational algebra is built on the assumption of linearity. By mastering f(x) = mx + b, students gain a powerful tool for predicting future outcomes based on current trends. This section simplifies the graphing process significantly, moving students away from tedious T-charts and toward a more sophisticated understanding of how "steepness" and "starting position" dictate the behavior of a function.
DOK Level 2
Level 2 (Skill/Concept): Using the slope and y-intercept to construct a graph. Students must also take a table of values and calculate the differences between outputs to determine if the function is truly linear. This requires comparing multiple pieces of information to verify a property.
Calculating slope as change in x over change in y, or calculating slope as the change between the coordinates of one point over change between the coordinates of a second point
If students automatically assume that the left-most point has to be (x1, y1) and the point farther right is (x2, y2), then explain that the designation of (x1, y1) and (x2, y2) is arbitrary. Write pairs of points on index cards. Give one card to each student. Have them find the slope both ways. Then ask which way made the subtraction easier.
Extension: The road sign on a hill says 5% grade. The elevation of the road at that point is 1200 feet. Make a drawing of this situation. What would be the elevation of the road at an additional 2000 horizontal feet from the road sign?
Use "you try" pg 210 and practice problems to assess students' understanding of the lesson concepts