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Mathematics LibreTexts

4.1E: Linear Functions (Exercises)

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1. Determine whether the algebraic equation is linear. 2x+3y=7
2. Determine whether the algebraic equation is linear. 6x2y=5
3. Determine whether the function is increasing or decreasing. f(x)=7x2


4. Determine whether the function is increasing or decreasing. g(x)=x+2

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 1st , 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 nth  day after June 1st  ?

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

13. 2x6y=12x+3y=1

14 y=13x23x+y=9

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

15. 7x+9y=63
16. f(x)=2x1

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)=5x1 and passing through the point (5,20).

20. Find the equation of a line with a y - intercept of (0,2) and slope 12.

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?


This page titled 4.1E: Linear Functions (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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