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Mathematics LibreTexts

4.1E: Linear Functions (Exercises)

  • Page ID
    56076
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    1. Determine whether the algebraic equation is linear. \(2 x+3 y=7\)
    2. Determine whether the algebraic equation is linear. \(6 x^{2}-y=5\)
    3. Determine whether the function is increasing or decreasing. \[f(x)=7 x-2 \nonumber\]
    4. Determine whether the function is increasing or decreasing. \[g(x)=-x+2 \nonumber\]
    5. Given each set of information, find a linear equation that satisfies the given conditions, if possible.
    Passes through (7,5) and (3,17)
    6. Given each set of information, find a linear equation that satisfies the given conditions, if possible.
    \(x\) -intercept at (6,0) and \(y\) -intercept at (0,10)
    7. Find the slope of the line shown in the graph.

    This is a graph of an increasing line with a y-intercept of -3 and x-intercept of 1 on an x, y coordinate plane.  The x and y-axis range from -6 to 6.

     

    8

    This is a graph of a line with a y-intercept of -2 and no x-intercepts on an x, y coordinate plane.  The x- and y-axis range from -6 to 6

    9.

    This is a graph of a line with a y-intercept of -2 and x-intercept of 1 on an x, y coordinate plane.  The x- and y-axis both range from -6 to 6.

    10

    Does the following table represent a linear function? If so, find the linear equation that models the data.

    x –4 0 2 10
    g(x) 18 –2 –12 –52

    Does the following table represent a linear function? If so, find the linear equation that models the data.

    x 6 8 12 26
    g(x) –8 –12 –18 –46

    12. On June \(1^{\text {st }}\), a company has \(\$ 4,000,000\) profit. If the company then loses 150,000 dollars per day thereafter in the month of June, what is the company's profit \(n^{\text {th }}\) day after June \(1^{\text {st }}\) ?

    For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

    13. \[\begin{align*} 2 x-6 y &=12 \\[4pt] -x+3 y &=1 \end{align*}\]

    14 \[\begin{align*} y &=\frac{1}{3} x-2 \\[4pt] 3 x+y &=-9 \end{align*}\]

    For the following exercises, find the \(x\) - and \(y\) - intercepts of the given equation

    15. \(7 x+9 y=-63\)
    16. \(f(x)=2 x-1\)

    For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line \(2 .\) Is each pair of lines parallel, perpendicular, or neither?

    17.

    • Line 1 : Passes through (5,11) and (10,1)
    • Line 2: Passes through (-1,3) and (-5,11)

    18.

    • Line 1: Passes through (8,-10) and (0,-26)
    • Line 2: Passes through (2,5) and (4,4)

    19. Write an equation for a line perpendicular to \(f(x)=5 x-1\) and passing through the point (5,20).

    20. Find the equation of a line with a \(y\) - intercept of (0,2) and slope \(-\frac{1}{2}\).

    23. A car rental company offers two plans for renting a car.

    • Plan A: 25 dollars per day and 10 cents per mile
    • Plan B: 50 dollars per day with free unlimited mileage

    How many miles would you need to drive for plan B to save you money?