Chapter 4 Linear Functions
Chapter 4 Practice Test
For the following exercises, find the equation of the line with the given information.
- Passes through the points[latex]\,\left(-4,2\right)\,[/latex]and[latex]\,\left(5,-3\right).[/latex]
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[latex]y=\frac{-5}{9}x-\frac{2}{9}[/latex]
- Has an undefined slope and passes through the point[latex]\,\left(4,3\right).[/latex]
- Passes through the point[latex]\,\left(2,1\right)\,[/latex]and is perpendicular to[latex]\,y=\frac{-2}{5}x+3.[/latex]
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[latex]y=\frac{5}{2}x-4[/latex]
- Determine whether the following algebraic equation can be written as a linear function.[latex]\,2x+3y=7[/latex]
- Determine whether the following function is increasing or decreasing.[latex]\,f\left(x\right)=-2x+5[/latex]
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Decreasing
- Determine whether the following function is increasing or decreasing.[latex]f\left(x\right)=7x+9[/latex]
- Find a linear equation that passes through (5, 1) and (3, –9), if possible.
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[latex]y=5x-24[/latex]
- Find a linear equation that has an x intercept at (–4, 0) and a y-intercept at (0, –6), if possible.
- Find the slope of the line in Figure 1.
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[latex]m=-2[/latex]
- Write an equation for line in Figure 2.
- Does the table below represent a linear function? If so, find a linear equation that models the data.
| [latex]x[/latex] | –6 | 0 | 2 | 4 |
| [latex]g\left(x\right)[/latex] | 14 | 32 | 38 | 44 |
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Yes,[latex]\,y=3x+32[/latex]
- Does the table below represent a linear function? If so, find a linear equation that models the data.
| x | 1 | 3 | 7 | 11 |
| g(x) | 4 | 9 | 19 | 12 |
- At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hour for the remainder of the day, write an expression to represent the number of items that were sold[latex]\,n\,[/latex]after 6 am.
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[latex]y=30x+120[/latex]
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular.
- [latex]\begin{array}{c}y=\frac{3}{4}x-9\\ -4x-3y=8\end{array}[/latex]
- [latex]\begin{array}{c}-2x+y=3\\ 3x+\frac{3}{2}y=5\end{array}[/latex]
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Neither
- Find the x– and y-intercepts of the equation[latex]\,2x+7y=-14.[/latex]
- Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?
Line 1: Passes through[latex]\,\left(-2,-6\right)\,[/latex]and[latex]\,\left(3,14\right)[/latex]
Line 2: Passes through[latex]\,\left(2,6\right)\,[/latex]and[latex]\,\left(4,14\right)[/latex]
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Line 1:[latex]\,m=4;[/latex] Line 2:[latex]\,m=4;[/latex]parallel
- Write an equation for a line perpendicular to[latex]\,f\left(x\right)=4x+3\,[/latex]and passing through the point[latex]\,\left(8,10\right).[/latex]
- Sketch a line with a y-intercept of[latex]\,\left(0,\text{5}\right)\,[/latex]and slope[latex]\,-\frac{5}{2}.[/latex]
- Graph