Intermediate Algebra (11th edition)

The equation is called a first-degree equation,because it has no

term with a variable to a power greater than 1.

The graph of any first-degree equation in two variables is a straight line.

Since first-degree equations with two variables have straight-line graphs, they are

3.3 Linear Equations in Two Variables vi Contents

2 x+ 3 y= 6

SECTION 3.1 The Rectangular Coordinate System 139

*Some texts define an intercept as a number, not a point. For example, “y-intercept ” would be given as

“y-intercept 4.”

1 0, 4 2

Finding Intercepts

When graphing the equation of a line, find the intercepts as follows.

Let to find the x-intercept.

Let x= 0 to find the y-intercept.

y= 0

Linear Equation in Two Variables

A linear equation in two variablescan be written in the form

where A, B, and Care real numbers and Aand Bare not both 0. This form is

called standard form.

AxByC,

OBJECTIVE 5 Find x- and y-intercepts. A straight line is determined if any

two different points on the line are known. Therefore, finding two different points is

enough to graph the line.

Two useful points for graphing are the x- and y-intercepts. The x-interceptis

the point (if any) where the line intersects the x-axis. The y-interceptis the point

(if any) where the line intersects the y-axis.* See FIGURE 5.

The y-value of the point where the line intersects the x-axis is 0. Similarly, the

x-value of the point where the line intersects the y-axis is 0. This suggests a

method for finding the x- and y-intercepts.

Finding Intercepts

Find the x- and y-intercepts of 4 x-y=- 3 and graph the equation.

EXAMPLE 2

x

y

y-intercept

x-intercept

(^0) (a, 0)
(0, b)
FIGURE 5

To find the x-intercept, let

Let.

x-intercept is.

To find the y-intercept, let

Let.

y= 3 y-intercept is 1 0, 3 2.

- y=- 3

4102 - y=- 3 x= 0

4 x-y=- 3

x=0.

x =- A- 43 , 0B

3

4

4 x=- 3

4 x- 0 =- 3 y= 0

4 x-y=- 3

y=0.