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# 4.1E: Linear Functions (Exercises)


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.

8

9.

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?