Lesson 1: 3-1 Graphing Linear Functions

What are the benefits of having a model for a linear function?

What are the intercepts located on a graph?

Which intercept is located at the point where a line crosses the x-axis?

What is the value of the x-coordinate of the point where a line crosses the x-axis?

What is the value of the y-coordinate of the point where a line crosses the x-axis?

When given the quation of a linear function, what value do you substitute for x to find the y-intercept?

linear equation
standard form
constant
x-intercept
y-intercept

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

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

An equation is linear if the Properties of Equality can be applied to rewrite it in standard form. The graph of a linear function has at most one x-intercept and one y-intercept. The intercepts can be found by alternately replacing x and y with 0. Values of x for which y = 0 are called zeros. A zero is an x-intercept.

Recycling one ton of waste paper saves an average of 17 trees, 7000 gallons of water, 3 barrels of oil, and about 33 cubic yards of landfill space.

The relationship between the amount of paper recycled and the number of trees saved can be expressed with the equation y = 17x, where y represents the number of trees and x represents the ton of paper recycled.

Standard Form Students may assume that the standard form implies that linear equations must have positive coefficients on x and y. Point out that there are no restrictions on the value of B. This means that B could be negative. So, an equation like 3x - 4y = 7 is a linear equation.

If students have mastered graphing with whole-number intercepts, then give students an equation with at least one of the intercepts of the graph not a whole number. Have students suggest an easier way to graph the equation.

Extension: Explain to students that the graph of a linear equation is called a continuous graph. It represents all solutions of the linear equation. Every ordered pair on a continuous line satisfies the equation. When the variables in an equation must be whole numbers, the points cannot be connected with a line. This type of graph is a discrete graph. Ask students to think of an example of when a discrete graph would be used.

Exercises 65 - 68

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