Lesson 2: 3-2 Zeros of Linear Functions (intercepts)

Why is it helpful to have different ways to graph linear functions?

linear function
parent function
family of graphs
root

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25

The solution or root of an equation is any value that makes the equation true. A linear equation has none or one root. The root of a linear equation can be found by graphing the equation’s related function. When the graph is a line that does not intersect the x-axis, there is no solution. When the graph is a line that intersects the x-axis, there is one solution.

Maria can go 420 miles on a 12-gallon tank of gas. The equation y = 420 - 12x describes the distance she can travel on a full tank of gas if her fuel mileage is x miles per gallon. Find the zero and describe what it means in the context of the situation. Identify the domain and range.

Error Analysis: For Exercise 46, students should see that Clarissa did not simplify x + 5 = 4 correctly.

If students have difficulty graphing equations, then consider having them work in small groups to work on problems like Example 1b. Make a large coordinate grid on a tiled floor. Assign one or two group members to make a table of values. Then have students stand on the grid in the location of their ordered pairs and hold a string between them, close to the floor, to model the line. Have a student locate where the string crosses the x-axis.

Exercises 51-58

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