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__Quiz 9__

**1.)** Graph $2x+5y=3$.

*Solution:* First we find two solutions: let $x=0$ yielding the equation $5y=3$ which can be solved to get $y=\dfrac{3}{5}$. This means that $\left( 0, \dfrac{3}{5} \right)$ is a solution. Now let $y=0$ yielding the equation $2x=3$ which can be solved for $x =\dfrac{3}{2}$. This means that $\left( \dfrac{3}{2},0 \right)$ is a solution. Now plot these points and draw the line between them:

**2.)** Graph $x=17$.

*Solution:*

The following information is used in problems 3 and 4:

You rent a car with a full tank of gas on 7 August. You return it on 9 August. When you rented, the odometer read $5,710$ miles and when you returned it, the odometer read $5,790$ miles. When you returned it, you needed to put in $2$ gallons of gas.

**3.)** What was the gas mileage in terms of $\dfrac{\mathrm{miles}}{\mathrm{gallon}}$?

*Solution:* You travelled $5790-5710=80$ miles during your trip. The trip required $2$ gallons of gas.
Therefore the gas mileage was
$$\dfrac{80 \mathrm{\hspace{2pt} miles}}{2 \mathrm{\hspace{2pt} gallons}} = 40 \dfrac{\mathrm{miles}}{\mathrm{gallon}}.$$

**4.)** What was the (average) rate of travel in $\dfrac{\mathrm{miles}}{\mathrm{day}}$?

*Solution:* As discovered in the previous problem, you travelled $80$ miles. The trip took $9-7=2$ days.
Therefore the gas mileage was
$$\dfrac{80 \mathrm{\hspace{2pt} miles}}{2 \mathrm{\hspace{2pt} days}} = 40 \dfrac{\mathrm{miles}}{\mathrm{day}}.$$

**5.)** Find the slope of the line containing the points $(1,2)$ and $(1,-4)$.

*Solution:* This line is a vertical line. We said such lines have **infinite slope**. A calculation of the slope would yield
$$\mathrm{slope} = \dfrac{-4-2}{1-1} = \dfrac{-6}{0},$$
which is "a problem" because of the division by zero. We "interpret" this division by zero as $\infty$ because of our definition of the slope of a vertical line.