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[link] shows the input, $w,$ and output, $k,$ for a linear function $k.$ a. Fill in the missing values of the table. b. Write the linear function $k,$ round to 3 decimal places.
$w$ | –10 | 5.5 | 67.5 | b |
$k$ | 30 | –26 | a | –44 |
[link] shows the input, $p,$ and output, $q,$ for a linear function $q.$ a. Fill in the missing values of the table. b. Write the linear function $k.$
$p$ | 0.5 | 0.8 | 12 | b |
$q$ | 400 | 700 | a | 1,000,000 |
a. $a=11,900$ ; $b=1001.1$ b. $q(p)=1000p-100$
Graph the linear function $f$ on a domain of $\left[-10,10\right]$ for the function whose slope is $\frac{1}{8}$ and y -intercept is $\frac{31}{16}$ . Label the points for the input values of $-10$ and $10.$
Graph the linear function $f$ on a domain of $\left[-0.1,0.1\right]$ for the function whose slope is 75 and y -intercept is $-22.5$ . Label the points for the input values of $-0.1$ and $\mathrm{0.1.}$
Graph the linear function $f$ where $f\left(x\right)=ax+b$ on the same set of axes on a domain of $\left[-4,4\right]$ for the following values of $a$ and $b.$
Find the value of $x$ if a linear function goes through the following points and has the following slope: $(x,2),(-4,6),\text{\hspace{0.17em}}m=3$
$x=-\frac{16}{3}$
Find the value of y if a linear function goes through the following points and has the following slope: $(10,y),(25,100),\text{\hspace{0.17em}}m=-5$
Find the equation of the line that passes through the following points: $\left(a,\text{}b\right)$ and $\left(a,\text{}b+1\right)$
$x=a$
Find the equation of the line that passes through the following points: $\left(2a,\text{}b\right)$ and $\left(a,\text{}b+1\right)$
Find the equation of the line that passes through the following points: $\left(a,\text{}0\right)$ and $\left(c,\text{}d\right)$
$y=\frac{d}{c-a}x-\frac{ad}{c-a}$
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves $n$ more customers during her shift?
A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?
$45 per training session.
A clothing business finds there is a linear relationship between the number of shirts, $n,$ it can sell and the price, $p,$ it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $\$30$ , while 3,000 shirts can be sold at a price of $22. Find a linear equation in the form $p(n)=mn+b$ that gives the price $p$ they can charge for $n$ shirts.
A phone company charges for service according to the formula: $C(n)=24+0.1n,$ where $n$ is the number of minutes talked, and $C(n)$ is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.
A farmer finds there is a linear relationship between the number of bean stalks, $n,$ she plants and the yield, $y,$ each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form $y=\mathrm{mn}+b$ that gives the yield when $n$ stalks are planted.
A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
The slope is $-400.$ This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.
A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, $P\left(t\right),$ for the population $t$ years after 2003.
Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: $I(x)=1054x+23,286,$ where $x$ is the number of years after 1990. Which of the following interprets the slope in the context of the problem?
c.
When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of $C,$ the Celsius temperature, $F\left(C\right).$
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