Exam 1: Linear Functions and Change

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 60,000 dollars on advertising, it sold 680 cars. Moreover, for each additional 5 thousand dollars spent, they sell 40 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. What is the practical interpretation of the vertical intercept of the equation?

Find the equation of a line parallel to $y=\frac{3}{4} x-2$ and through the point $(3,0)$

If a linear population function is 50,000 in year $\mathrm{t}=0$ and grows by 1,250 people per year, then $P(t)=b+m t$ , where $b=―――$ and $m=―――$

Determine the slope of a line perpendicular to $y=\frac{7}{5} x-7$

What is the equation of the line with $x$ -intercept $x_{0}$ and $y$ -intercept $y_{0}$ ?

Find a formula for the linear function that passes through the points $(3,3)$ and $(-2,18)$ . Express your answer in $y=m x+b$ form.

The following table shows the cost of a cell phone bill, in dollars, as a function of the number of texts. Use a calculator program to find a linear regression line for this data.

ComElectric, the Cambridge power company, charges its customers $\$ 9.00$ a month and $\$ 0.0675$ per kwh, plus a $\$ 0.0315$ per kwh surcharge. (A kwh, or kilowatt-hour, is a unit of electricity supplied). The formula for the monthly cost for $x$ kwh of electricity is $C=b+m x$ dollars, where $b=―――$ and $m=―――$

Let $y=p(x)$ be defined by the following graph. Is $p(f / 2)$ closer to $g, h$ or $i$ ?

The following tables give the profits (in millions) of a manufacturing company $t$ months after January 1, 2008. t (months) 0 2 3 4 5 6 8 9 10 11 r (millions) 5.2 6.1 4.2 5.1 5.9 6.5 6.1 7.3 6.2 5.6 Use a calculator program to find the linear regression line for this data. What is the physical interpretation of the $t$ -intercept?

The table below gives the deer population in a state park. Based on the information in the chart, what would you predict about the deer population in this state park in the year 2020.

A cookie store has a fixed monthly cost of $\$ 540$ . It costs the cookie store $\$ 0.20$ to make a cookie and the store sells each cookie for $\$ 1.40$ . Express revenue R, cost C, and profit $\mathrm{P}$ for the cookie store when making and selling $x$ cookies in a month.

Which of the following figures shows the graph of a person's weight, $w$ , as a function of time $t$ , in months if the person starts out at 150 pounds and loses 5 pounds a month?

Suppose there are 100 people living in a small town and the rate of change of the town's population is 7 people per year. How many people will be living in the town twenty years from now?

What could the following graph reasonably represent?

If $f(x)$ is an increasing function, what can you say about $f(3)$ and $f(4)$ ?

The following figure show the distance of two horses from the starting point of a race as a function of time. Which horse was ahead for most of the race? (Answer "A" or "B")

At a price of $\$ 2.80$ per gallon, the average weekly demand by consumers for gasoline is 42 gallons. If the price rises to $\$ 3.00$ , the weekly demand drops to 39 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 slope $m$ , along with its economic significance?

Mark all of the following functions that pass through the point $(0,6)$ .

For the line $y+4=3 x-6$ , a) what is the slope of the line? b) what is the y-intercept of the line?