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Find the equation of the line that passes through the following points:
$\text{\hspace{0.17em}}\left(a,\text{}b\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(a,\text{}b+1\right)$
Find the equation of the line that passes through the following points:
$(2a,b)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}(a,b+1)$
$y=-\frac{1}{2}x+b+2$
Find the equation of the line that passes through the following points:
$(a,0)$ and $\text{\hspace{0.17em}}(c,d)$
Find the equation of the line parallel to the line $\text{\hspace{0.17em}}g\left(x\right)=\mathrm{-0.}\text{01}x\text{+2}\text{.01}\text{\hspace{0.17em}}$ through the point $\text{\hspace{0.17em}}(1,\text{2}).$
y = –0.01 x + 2.01
Find the equation of the line perpendicular to the line $\text{\hspace{0.17em}}g\left(x\right)=\mathrm{-0.}\text{01}x\text{+2}\text{.01}\text{\hspace{0.17em}}$ through the point $\text{\hspace{0.17em}}(1,\text{2}).$
For the following exercises, use the functions $\text{\hspace{0.17em}}f\left(x\right)=\mathrm{-0.}\text{1}x\text{+200and}g\left(x\right)=20x+\mathrm{0.1.}$
Find the point of intersection of the lines $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}g.$
$\text{}\left(\frac{1999}{201},\frac{400,001}{2010}\right)$
Where is $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ greater than $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ Where is $\text{\hspace{0.17em}}g\left(x\right)\text{\hspace{0.17em}}$ greater than $\text{\hspace{0.17em}}f\left(x\right)?$
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 $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ more customers during her shift?
$20+0.5n$
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?
A clothing business finds there is a linear relationship between the number of shirts, $\text{\hspace{0.17em}}n,$ it can sell and the price, $\text{\hspace{0.17em}}p,$ it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $\text{\hspace{0.17em}}\$30,$ while 3,000 shirts can be sold at a price of $22. Find a linear equation in the form $\text{\hspace{0.17em}}p(n)=mn+b\text{\hspace{0.17em}}$ that gives the price $\text{\hspace{0.17em}}p\text{\hspace{0.17em}}$ they can charge for $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ shirts.
$p(n)=-0.004n+34$
A phone company charges for service according to the formula: $\text{\hspace{0.17em}}C(n)=24+0.1n,$ where $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is the number of minutes talked, and $\text{\hspace{0.17em}}C(n)\text{\hspace{0.17em}}$ is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
A farmer finds there is a linear relationship between the number of bean stalks, $\text{\hspace{0.17em}}n,$ she plants and the yield, $\text{\hspace{0.17em}}y,$ 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 $\text{\hspace{0.17em}}y=mn+b\text{\hspace{0.17em}}$ that gives the yield when $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ stalks are planted.
$y=-0.5n+45$
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.
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, $\text{\hspace{0.17em}}P(t),$ for the population $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ years after 2003.
$P(t)=1700t+45,000$
Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: $\text{\hspace{0.17em}}I(x)=1054x+23,286,$ where $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ is the number of years after 1990. Which of the following interprets the slope in the context of the problem?
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 $\text{\hspace{0.17em}}C,$ the Celsius temperature, $\text{\hspace{0.17em}}F\left(C\right).$
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