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    Graphs and Graphing

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    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

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    Solution Summary

    Nineteen problems dealing with graphs and graphing are solved.

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