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Terry is skiing down a steep hill. Terry's elevation, $E(t),$ in feet after $t$ seconds is given by $E(t)=3000-70t.$ Write a complete sentence describing Terry’s starting elevation and how it is changing over time.
Terry starts at an elevation of 3000 feet and descends 70 feet per second.
Maria is climbing a mountain. Maria's elevation, $E(t),$ in feet after $t$ minutes is given by $E(t)=1200+40t.$ Write a complete sentence describing Maria’s starting elevation and how it is changing over time.
Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?
3 miles per hour
Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. Write an equation for her distance from home t hours from now.
A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.
$d\left(t\right)=100-10t$
Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding $n$ rides?
For the following exercises, determine whether the equation of the curve can be written as a linear function.
$3x+5y=15$
$3x+5{y}^{2}=15$
$-\frac{x-3}{5}=2y$
For the following exercises, determine whether each function is increasing or decreasing.
$g\left(x\right)=5x+6$
$b\left(x\right)=8-3x$
$k\left(x\right)=-4x+1$
$p\left(x\right)=\frac{1}{4}x-5$
$m\left(x\right)=-\frac{3}{8}x+3$
For the following exercises, find the slope of the line that passes through the two given points.
$\left(1,\text{5}\right)$ and $\left(4,\text{11}\right)$
$(\mathrm{-1},\text{4})$ and $(5,\text{2})$
$\u2013\frac{1}{3}$
$(8,\mathrm{-2})$ and $(4,6)$
For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
$f(-5)=-4,$ and $f(5)=2$
$f(\mathrm{-1})=4$ and $f(5)=1$
$f(x)=-\frac{1}{2}x+\frac{7}{2}$
$(2,4)$ and $(4,10)$
Passes through $\left(-1,\text{4}\right)$ and $\left(5,\text{2}\right)$
Passes through $\left(-2,\text{8}\right)$ and $\left(4,\text{6}\right)$
$y=-\frac{1}{3}x+\frac{22}{3}$
x intercept at $\left(-2,\text{0}\right)$ and y intercept at $(0,\mathrm{-3})$
x intercept at $\left(-5,\text{0}\right)$ and y intercept at $\left(0,\text{4}\right)$
$y=\frac{4}{5}x+4$
For the following exercises, find the slope of the lines graphed.
For the following exercises, write an equation for the lines graphed.
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, $g(x)=-3x+5$
$x$ | 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, $f(x)=5x-5$
$$x$$ | 5 | 10 | 20 | 25 |
$$k\left(x\right)$$ | 28 | 13 | 58 | 73 |
$$x$$ | 0 | 2 | 4 | 6 |
$$g\left(x\right)$$ | 6 | –19 | –44 | –69 |
Linear, $g(x)=-\frac{25}{2}x+6$
$$x$$ | 2 | 4 | 6 | 8 |
$$f\left(x\right)$$ | –4 | 16 | 36 | 56 |
$$x$$ | 2 | 4 | 6 | 8 |
$$f\left(x\right)$$ | –4 | 16 | 36 | 56 |
Linear, $f(x)=10x-24$
$$x$$ | 0 | 2 | 6 | 8 |
$$k\left(x\right)$$ | 6 | 31 | 106 | 231 |
If $f$ is a linear function, $f(0.1)=11.5,\text{and}f(0.4)=\u20135.9,$ find an equation for the function.
$f(x)=-58x+17.3$
Graph the function $f$ on a domain of $\left[\u201310,10\right]:f(x)=0.02x-\mathrm{0.01.}$ Enter the function in a graphing utility. For the viewing window, set the minimum value of $x$ to be $-10$ and the maximum value of $x$ to be $10.$
Graph the function $f$ on a domain of $\left[\u201310,10\right]:fx)=2,500x+4,000$
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