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Write an equation for a line perpendicular to $\text{\hspace{0.17em}}h(t)=\mathrm{-2}t+4\text{\hspace{0.17em}}$ and passing through the point $\text{\hspace{0.17em}}(\mathrm{-4},\mathrm{\u20131}).$
Write an equation for a line perpendicular to $\text{\hspace{0.17em}}p(t)=3t+4\text{\hspace{0.17em}}$ and passing through the point $\text{\hspace{0.17em}}(3,1).$
$y=-\frac{1}{3}t+2$
For the following exercises, find the slope of the line graphed.
For the following exercises, write an equation for the line graphed.
For the following exercises, match the given linear equation with its graph in [link] .
$f\left(x\right)=-x-1$
$f\left(x\right)=-\frac{1}{2}x-1$
$f\left(x\right)=2+x$
For the following exercises, sketch a line with the given features.
An x -intercept of $\text{\hspace{0.17em}}(\mathrm{\u20134},\text{0})\text{\hspace{0.17em}}$ and y -intercept of $\text{\hspace{0.17em}}(0,\text{\u20132})$
An x -intercept $\text{\hspace{0.17em}}(\mathrm{\u20132},\text{0})\text{\hspace{0.17em}}$ and y -intercept of $\text{\hspace{0.17em}}(0,\text{4})$
A y -intercept of $\text{\hspace{0.17em}}(0,\text{7})\text{\hspace{0.17em}}$ and slope $\text{\hspace{0.17em}}-\frac{3}{2}$
A y -intercept of $\text{\hspace{0.17em}}(0,\text{3})\text{\hspace{0.17em}}$ and slope $\text{\hspace{0.17em}}\frac{2}{5}$
Passing through the points $\text{\hspace{0.17em}}(\mathrm{\u20136},\text{\u20132})\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}(6,\text{\u20136})$
Passing through the points $\text{\hspace{0.17em}}(\mathrm{\u20133},\text{\u20134})\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}(3,\text{0})$
For the following exercises, sketch the graph of each equation.
$f\left(x\right)=\mathrm{-2}x-1$
$f\left(x\right)=\frac{1}{3}x+2$
$f\left(t\right)=3+2t$
$r\left(x\right)=4$
For the following exercises, write the equation of the line shown in the graph.
For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.
$x$ | 0 | 5 | 10 | 15 |
$g\left(x\right)$ | 5 | –10 | –25 | –40 |
Linear, $\text{\hspace{0.17em}}g(x)=-3x+5$
$x$ | 0 | 5 | 10 | 15 |
$h\left(x\right)$ | 5 | 30 | 105 | 230 |
$x$ | 0 | 5 | 10 | 15 |
$f\left(x\right)$ | –5 | 20 | 45 | 70 |
Linear, $\text{\hspace{0.17em}}f(x)=5x-5$
$x$ | 5 | 10 | 20 | 25 |
$k\left(x\right)$ | 13 | 28 | 58 | 73 |
$x$ | 0 | 2 | 4 | 6 |
$g\left(x\right)$ | 6 | –19 | –44 | –69 |
Linear, $\text{\hspace{0.17em}}g(x)=-\frac{25}{2}x+6$
$x$ | 2 | 4 | 8 | 10 |
$h\left(x\right)$ | 13 | 23 | 43 | 53 |
$x$ | 2 | 4 | 6 | 8 |
$f\left(x\right)$ | –4 | 16 | 36 | 56 |
Linear, $\text{\hspace{0.17em}}f(x)=10x-24$
$x$ | 0 | 2 | 6 | 8 |
$k\left(x\right)$ | 6 | 31 | 106 | 231 |
For the following exercises, use a calculator or graphing technology to complete the task.
If $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ is a linear function, $\text{\hspace{0.17em}}f(0.1)=11.5,\text{and}f(0.4)=\mathrm{\u20135.9},\text{\hspace{0.17em}}$ find an equation for the function.
$f(x)=-58x+17.3$
Graph the function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}[\mathrm{\u201310},10]:f(x)=0.02x-\mathrm{0.01.}\text{\hspace{0.17em}}$ Enter the function in a graphing utility. For the viewing window, set the minimum value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ to be $\text{\hspace{0.17em}}\mathrm{-10}\text{\hspace{0.17em}}$ and the maximum value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ to be $\text{\hspace{0.17em}}10.$
Graph the function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}[\mathrm{\u201310},10]:fx)=2,500x+4,000$
[link] shows the input, $\text{\hspace{0.17em}}w,$ and output, $\text{\hspace{0.17em}}k,$ for a linear function $\text{\hspace{0.17em}}k.\text{\hspace{0.17em}}$ a. Fill in the missing values of the table. b. Write the linear function $\text{\hspace{0.17em}}k,$ round to 3 decimal places.
w | –10 | 5.5 | 67.5 | b |
k | 30 | –26 | a | –44 |
$y=3.613x-6.129\text{}$
[link] shows the input, $\text{\hspace{0.17em}}p,$ and output, $\text{\hspace{0.17em}}q,$ for a linear function $\text{\hspace{0.17em}}q.\text{\hspace{0.17em}}$ a. Fill in the missing values of the table. b. Write the linear function $\text{\hspace{0.17em}}k.$
p | 0.5 | 0.8 | 12 | b |
q | 400 | 700 | a | 1,000,000 |
Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[-10,10\right]\text{\hspace{0.17em}}$ for the function whose slope is $\text{\hspace{0.17em}}\frac{1}{8}\text{\hspace{0.17em}}$ and y -intercept is $\text{\hspace{0.17em}}\frac{31}{16}.\text{\hspace{0.17em}}$ Label the points for the input values of $\text{\hspace{0.17em}}\mathrm{-10}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}10.$
Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ on a domain of $\text{\hspace{0.17em}}\left[-0.1,0.1\right]\text{\hspace{0.17em}}$ for the function whose slope is 75 and y -intercept is $\text{\hspace{0.17em}}\mathrm{-22.5.}\text{\hspace{0.17em}}$ Label the points for the input values of $\text{\hspace{0.17em}}\mathrm{-0.1}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\mathrm{0.1.}$
Graph the linear function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}f\left(x\right)=ax+b\text{\hspace{0.17em}}$ on the same set of axes on a domain of $\text{\hspace{0.17em}}\left[-4,4\right]\text{\hspace{0.17em}}$ for the following values of $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b.$
Find the value of $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ if a linear function goes through the following points and has the following slope: $\text{\hspace{0.17em}}(x,2),(\mathrm{-4},6),\text{\hspace{0.17em}}m=3$
Find the value of y if a linear function goes through the following points and has the following slope: $\text{\hspace{0.17em}}(10,y),(25,100),\text{\hspace{0.17em}}m=\mathrm{-5}$
y = 175
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