Temperatures and traveling When U.S. citizens travel abroad, they need some understanding of Celsius temperature readings-does one need mittens if the temperature will be $20^{\circ} \mathrm{C}$ ? A quick conversion formula often used by tour guides to give a rough Fahrenheit equivalent for a Celsius reading is

$$F=2 C+30 \quad \text { Tourist formula }$$

The exact conversion formula relating these readings is

$$F=1.8 C+32 \quad \text {Scientific formula}$$

(a) At what temperatures, Fahrenheit and Celsius, do these formulas agree?

(b) As the Celsius temperature rises above the reading found in part (a), does the tourist formula overestimate or underestimate the actual Fahrenheit temperature? How can you tell this from the two given formulas?

If the demand function and supply function for Z-brand juicers are $p+2 q=100$ and $35 p-20 q=350$, respectively, compare the quantity demanded and the quantity supplied when $p=14$. Are there surplus juicers or not enough to meet demand?

Write the equation of the line that passes through the given point and has the given slope. Then graph the line.

$(1,1)$ with $0$ slope

Write the equation of each line described.

Through $(-2,7)$ and $(6,-4)$

A function and its graph are given. In each problem, find the domain.

$$f(x)=-2-\sqrt{9-x^2}$$

Write the equation of each line described.

Through $(-2,1)$ with slope $\frac{2}{5}$

A function and its graph are given. In each problem, find the domain.

$$f(x)=4+\sqrt{49-x^2}$$

Write the equation of the line that passes through the given point and has the given slope. Then graph the line.

$(-1,1)$ with undefined slope

Use the left-to-right elimination method to solve the systems.

$$\left\{\begin{array}{r}x-3 y-z=0 \\ x-2 y+z=8 \\ 2 x-6 y+z=6\end{array}\right.$$

Solve each inequality.

$$2(x+1)>x-1$$

Graph each function using a window that gives a complete graph.

$$y=\frac{x^2\ -\ x\ -\ 6}{x^2\ +\ 5x\ +\ 6}$$

If the demand for a pair of shoes is given by $2 p+5 q=200$ and the supply function for it is $p-2 q=10$, compare the quantity demanded and the quantity supplied when the price is $\$ 60$. Will there be a surplus or shortfall at this price?

Solve each inequality.

$$3(x-1)<2 x-1$$

Write the equation of the line that passes through the given point and has the given slope. Then graph the line.

$(3,-1)$ with slope $1$