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?