Exam 1: Linear Functions and Change

It costs $\$ 15$ to operate a lemonade stand, while a cup of lemonade sells for $\$ 0.75$ . Which of the following expresses the profit, $P$ , as a function of the number of cups, $c$ , of lemonade sold.

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.

Let $y=b+m x$ be the formula for the linear function defined in the following table. $b=―――$ and $m=―――$

Let $y=b+m x$ define a linear function with slope $1 /4$ that passes through the point (-1, 3). Then $b=―――$ and $m=―――$

An airplane has room for 300 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 $y=b+m x$ , then $b=―――$ and $m=―――$

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. From the formula for the regression line, estimate the value of $m$ that satisfies $C(m)=71.50$ . Round up to the nearest number of texts.

Suppose that $f(x)$ is linear, passes through the point $(6,-7)$ , and is parallel to $y=3-0.5 x$ . If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Find the equation of the line shown.