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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

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

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

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

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.