Exam 1: Linear Functions and Change

The following table gives the number $P$ of people living in a town $t$ years after 1990 . Use a calculator program to find the linear regression line for this data and use this to estimate how many lived in the year 2009. Round to the nearest whole number.

If a linear population function is 80,000 in year $\mathrm{t}=0$ and 87,500 by year $t=10$ , then $P(t)=b+m t$ , where $b=―――$ and $m=―――$

The following chart gives the number of students in a class that are a specific height in inches a) Is the number of students in each category a function of the height? b) Is the height in each category a function of the number of students in that category?

The cost, $\mathrm{C}$ , of producing $q$ items is given by the formula $C=C_{0}+m q$ , where $C_{0}$ and $m$ are positive constants. If the quantity produced decreases, what happens to the cost of production?

If the linear equation $-3 x+4 y+1=3 x$ is written in the form $y=b+m x$ , then $b=―――$ and $m=―――$

The following table shows the size of a cell phone bill, in dollars, as a function of the number of text messages. Use a calculator program to find a linear regression line for this data. Estimate $C(37)$ using the formula for the regression line.

Find a formula for the linear function that passes through the point $(3,14)$ with slope 5 . Express your answer in $y=m x+b$ form.

An airplane has room for 360 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with $x$ coach-fare seats and $y$ first-class seats, with no space wasted. If you found a formula for $y$ as a function of $x$ , what would be the significance of the $y$ -intercept?

Let $y=p(x)$ be defined by the following graph. Which of the following are true?

Find the formula for a linear function such that $f(18)=-4$ and $f(36)=-2$ .

Find the equation of a line parallel to $y=\frac{1}{2} x-6$ and through the point $(6,-7)$

The following chart gives the number of students in a class that are a specific height in inches a) What is the most common height of students in this class? b) What is the least common height of students in this class?

Several years ago, the wild rabbits of Australia were seriously threatened by a virus that was accidentally released into their population. Suppose that the following table gives the number $r$ of rabbits (in millions) remaining $t$ months after the release of the virus. Use a calculator program to find the linear regression line for this data. What is the physical interpretation of the $t$ -intercept?

Does an $r$ value of 0.03 seem reasonable for the following set of data?

Find the equation of the line shown.

Suppose that $f(x)$ is linear, has slope -1 , and forms the hypotenuse of the right triangle lying in Quadrant I whose area is 32 and whose legs lie on the $x$ and $y$ axes. If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Match the graph to the system of linear inequalities it represents

Solve $f(x)=0$ for $x$ using the graph of $f(x)$ below.

A box with volume $180 \mathrm{ft}^{3}$ has a square base of side length $s \mathrm{ft}$ and a height of $h \mathrm{ft}$ . Write a formula for the height of the box as a function of the side length of the box.

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 50,000 dollars on advertising, it sold 425 cars. Moreover, for each additional 10 thousand dollars spent, they sell 15 more cars. Let $y=b+m x$ be the formula for the number of cars sold as a function of $x$ , the amount of money spent on advertising. Then $b=―――$ and $m=―――$