Exam 1: Linear Functions and Change

Let $y=b+m x$ define a linear function with $y$ -intercept -3 that passes through the point $(-5,7)$ . Then $b=―――$ and $m=―――$

The following table gives the profits (in millions) of a manufacturing company $t$ months after January 1, 2008. Use a calculator program to find the linear regression line for this data and use this to estimate the profit on January 1, 2009. Round your answer to one decimal place.

It costs $\$ 10$ to operate a lemonade stand, while a cup of lemonade sells for $\$ 0.25$ . How many cups of lemonade must be sold in order to have $\$ 13.25$ in profit?

Mark all of the following functions that are increasing.

Rewrite the equation in slope-intercept form. $\frac{8 x+y}{3}=6$

The table below gives the deer population in a state park. year 1985 1990 number of deer 126 126 Using the table, find the average rate of change of the population over the interval 1990 to 2000 .

In 2006 , you earned $\$ 8.50$ per hour at your job. In 2009 , you earned $\$ 8.70$ per hour at your job. In 2010, you earned $\$ 9.30$ per hour at your job. a) What was the average rate of change in the amount you earned per hour between 2006 and 2009 ? b) What was the average rate of change in the amount you earned per hour between 2009 and 2010 ? Round answers to 3 decimal places if necessary.

Mark all of the following functions that have graphs that are parallel.

It costs a band $\$ 550$ to pay to rent a hall. They sell tickets for $\$ 10$ . How much profit, $P$ , will the band make if 300 people are attending the concert?

Could the following table represent a linear function?

You are looking at a graph of $P$ , a function of $t$ . Is it possible for the graph to intercept the $P$ -axis 5 times?

Let $f(x)=x^{3}$ . Find the average rate of change of the function $f$ between $x=3$ and $x=8$ .

Suppose that $f(x)$ is linear with an $x$ -intercept of -6 and parallel to $y=-4+0.5 x$ . If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

It costs a band $\$ 550$ to pay to rent a hall. They sell tickets for $\$ 20$ . Express the profit, $P$ , as a function of the number of people, $n$ , attending the concert.

Suppose that $f(x)$ is linear with slope -2 and passing through the point $(5,-16)$ . If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Suppose there are 150 people living in a small town and the rate of change of the town's population is -9 people per year. Which of the following must be true?

The following table gives the number $P$ of people living in a town $t$ years after 1990 . t (years) 1 4 7 8 10 12 14 17 18 24 r 4501 4512 4590 4480 4496 4590 4610 4610 4580 4510 Use a calculator program to find the slope of the linear regression line for this data. Round to 3 decimal places.

Line $\mathrm{A}$ in the figure is parallel to line $\mathrm{B}$ and line $\mathrm{A}$ has equation $y=\frac{3}{4} x+3$ . If point $\mathrm{C}$ is $(0,-3)$ , find the coordinate of point $\mathrm{D}$ .

If $f(2)>f(3.2)$ , then the function must be a decreasing function.

At a price of $\$ 2.75$ per gallon, the average weekly demand by consumers for gasoline is 45 gallons. If the price rises to $\$ 2.85$ , the weekly demand drops to 41 gallons. Assuming demand is linear, let $Q=b+m p$ , where $Q$ is the weekly quantity of gasoline demanded and $p$ is the price per gallon. What is the economic interpretation of the $p$ -intercept?