Intermediate Algebra (11th edition)

SECTION 3.1 The Rectangular Coordinate System 143

When graphing with a graphing calculator, we must tell the calculator how to set

up a rectangular coordinate system. In the screen in FIGURE 11, we chose minimum

x- and y-values of and maximum x- and y-values of 10. The scaleon each axis

determines the distance between the tick marks. In the screen shown, the scale is 1

for both axes. We refer to this screen as the standard viewing window.

To graph an equation such as , we use the intercepts to determine an

appropriate window. Here, the x-intercept is and the y-intercept is

Although many choices are possible, we choose the standard viewing window.

We must solve the equation for yto enter it into the calculator.

Subtract

Multiply by.

The graph in FIGURE 12also gives the intercepts at the bottoms of the screens. Some

calculators have the capability of locating the x-intercept (called “Root” or “Zero”).

Consult your owner’s manual.

y= 4 x- 3 - 1

- y=- 4 x+ 3 4 x.

4 x- y= 3

1 0.75, 0 2 1 0, - 32.

4 x-y= 3

- 10

CONNECTIONS

–10

• 10 10

10

Standard viewing window

FIGURE 11

• 10 10

–10

10

–10

Y = 4X – 3

• 10 10

–10

Y = 4X – 3 10

(a)

For Discussion or Writing

1. The graphing calculator screens in Exercise 73on page 146show the graph of a

linear equation. What are the intercepts?

Graph each equation with a graphing calculator. Use the standard viewing window.

2. 4 x- y=- 3 (Example 2) 3. x+ 2 y= 0 (Example 5)

Complete solution available
on the Video Resources on DVD

3.1 EXERCISES

Solve each problem by locating ordered pairs on the graphs. See Objective 1.

1.The graph indicates higher education financial

aid in billions of dollars.

(a)If the ordered pair represents a point

on the graph, what does xrepresent? What

does yrepresent?

(b)Estimate higher education aid in 2007.

(c)Write an ordered pair that gives

approximate aid in 2007.

(d)What does the ordered pair

mean in the context of this graph?

1 1997, 75 2

1 x, y 2

1 x, y 2

1992 1997 2002 2007

Aid (in billions

of dollars)

Source: The College Board.

Higher Education Aid

Year

50

100

150

200

(b)

FIGURE 12

NOTE When finding the coordinates of the midpoint of a line segment, we are finding

the averageof the x-coordinates and the averageof the y-coordinates of the endpoints of

the segment. In both cases, add the corresponding coordinates and divide the sum by 2.