Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.2 Linear Functions and Their Graphs

Linear Equation in Two Variables

• What did linear equation mean in Section 6.2?

• Ax + By = C• The graph of a linear equation in two

variables is a straight line.

Locating Intercepts

Since a linear equation is a straight line, its graph is determined by any two distinct solutions to the equation.

X-intercept, where the graph crosses the x axis

Y-intercept, where the graph crosses the y axis

To locate the x-intercept, set y=0 and solve the equation for x.

To locate the y-intercept, set x=0 and solve the equation for y.

Example: Locating Intercepts

Exercise Set 7.2 #5

Use the x and y intercepts to graph 2x + y = 6

Slope Concepts

• Slope provides a numerical measure for the steepness of a line.

• A steep line has a large slope.• A horizontal line has a slope of 0.• A line that goes top-left to bottom

right has a negative slope.• A vertical line has an undefined

slope

Definition of Slope

The slope of a line through the distinct points (x1, y1) and (x2, y2) is

)(

)(

12

12

xx

yy

Run

Rise

xinChange

yinChange

where x2 - x1 ≠ zero.

Example: Slope

Exercise Set 7.2 #13

Calculate the slope of the line passing through (-2, 4) and (-1, -1). Does this line rise, fall, or is it vertical or horizontal?

Slope-Intercept Form of the Equation of a Line

A linear equation of the form

y = mx + b

is said to be in slope-intercept form. • The coefficient of x is the slope of the line (m).• The constant term is its y-intercept (b).

Example: Slope-intercept

Exercise Set 7.2 #25, #37

Graph the following equations using the slope and y-intercept

32

32

1

yx

xy

Horizontal Line

The graph ofy = b

is a horizontal line. • The y-intercept is b.• In particular, the graph of y = 0 is the x-axis.• The slope of a horizontal line is 0

Exercise Set 7.2 #43

Graph y = -2

Vertical Line

The graph ofx = a

is a vertical line. • The x-intercept is a. • In particular, the graph of x = 0 is the y-axis.• The slope of a vertical line is undefined.

Exercise Set 7.2 #45

Graph x = 2

Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.2 Linear Functions and Their Graphs