일차함수와 그래프

Find the value of $x$ if a linear function goes through the following points and has the following slope: $(x,2),(-4,6),\,m=3$

Find the value ofy if a linear function goes through the following points and has the following slope: $(10,y),(25,100),\,m=-5$

Find the equation of the line that passes through the following points:

$(a,\,b)$ and $(a,\,b+1)$

Find the equation of the line that passes through the following points:

$(2a,b)$ and $(a,b+1)$

Find the equation of the line that passes through the following points:

$(a,0)$ and $(c,d)$

Find the equation of the line parallel to the line $g(x)=-0.01x+2.01$ through the point $(1,2).$

Find the equation of the line perpendicular to the line $g(x)=-0.01x+2.01$ through the point $(1,2).$

For the following exercises, use the functions $f(x)=-0.1x\text{+200 and }g(x)=20x+0.1.$

Find the point of intersection of the lines $f$ and $g.$

For the following exercises, use the functions $f(x)=-0.1x\text{+200 and }g(x)=20x+0.1.$

Where is $f(x)$ greater than $g(x)?$ Where is $g(x)$ greater than $f(x)?$

At noon, a barista notices that they have $20 in their tip jar. If the barista makes an average of $0.50 from each customer, how much will they have in the tip jar if they serve $n$ more customers during the shift?

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 $\text{\textdollar}30,$ 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 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 $y=mn+b$ that gives the yield when $n$ stalks are planted.

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?

• ⓐAs of 1990, average annual income was $23,286.
• ⓑIn the ten-year period from 1990–1999, average annual income increased by a total of $1,054.
• ⓒEach year in the decade of the 1990s, average annual income increased by $1,054.
• ⓓAverage annual income rose to a level of $23,286 by the end of 1999.

Explain how to find the input variable in a word problem that uses a linear function.

Explain how to find the output variable in a word problem that uses a linear function.

Explain how to interpret the initial value in a word problem that uses a linear function.

Explain how to determine the slope in a word problem that uses a linear function.

For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

Find the linear function that models the baby’s weight $W$ as a function of the age of the baby, in months, $t.$

For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

Find a reasonable domain and range for the function $W.$

For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

If the function $W$ is graphed, find and interpret the x- and y-intercepts.