# Graphs and Graphing

Complete each ordered pair so that it satisfies the given equation.

1.) y = 2 x + 5: (8, ), (-1, ), ( , -1)

Graph each equation. Plot at least five points for each equation.

Use graph paper. See Examples 3–5. If you have a graphing

calculator, use it to check your graphs when possible

2.) x - 2y = 6

3.) Dental services. The national cost C in billions of dollars

for dental services can be modeled by the linear equation

C =2.85n +30.52,

where n is the number of years since 1990 (Health Care

Financing Administration, www.hcfa.gov).

a) Find and interpret the C-intercept for the line.

b) Find and interpret the n-intercept for the line.

c) Graph the line for n ranging from 0 through 20.

Graph the line with the given point and slope.

4.) The line through (-2, 5) with slope-1

Solve each problem.

5.) Draw l1 through (-4, 0) and (0, 6). What is the slope of any

line parallel to l1? Draw l2 through the origin and parallel to l1.

Find the slope and y-intercept for each line that has a slope

and y-intercept.

6.) x+ 2y = 3

Graph each line using its y-intercept and slope.

7.) y + 4x = 8

In each case determine whether the lines are parallel,

perpendicular, or neither

8.) y = x + 7

y = x + 2

Write each equation in slope-intercept form.

9.) y + 3 = -3(x - 6)

Find the equation of the line that goes through the given point

and has the given slope. Write the answer in slope-intercept

form.

10.) (-1, -5), -8

Find the equation of each line. Write each answer in slopeintercept

form.

11.) The line is parallel to -3x + 2y = 9 and contains the point

(-2, 1).

Find the equation of each line in the form y = mx + b if

possible.

12.) The line through (3, 2) with undefined slope

13.) Basal energy requirement. The basal energy requirement

B is the number of calories that a person needs to maintain

the life process. For a 28-year-old female with a height of

160 centimeters and a weight of 45 kilograms (kg), B is

1300 calories. If her weight increases to 50 kg, then B is

1365 calories. There is a linear equation that expresses B in

terms of her weight w. Find the equation and find the basal

energy requirement if her weight is 53.2 kg.

Write a formula that expresses the relationship described by

each statement. Use k for the constant in each case.

14.) m varies directly as p.

15.) u varies inversely as n.

Find the variation constant, and write a formula that expresses

the indicated variation.

16.) c varies inversely as d, and c = 5 when d = 2.

Solve each variation problem.

17.) n varies directly as q, and n = 39 when q = 3. Find n

when q =8.

18.) Gas laws. The volume of a gas is inversely proportional to

the pressure on the gas. If the volume is 6 cubic centimeters

when the pressure on the gas is 8 kilograms per square

centimeter, then what is the volume when the pressure is

12 kilograms per square centimeter?

Graph each inequality.

19.) y < 2x + 2

#### Solution Summary

Nineteen problems dealing with graphs and graphing are solved.