To find the number of points awarded per correct answer, notice that the units of the slope are

\[ \dfrac{\textrm{points}}{\textrm{correct answers}}, \]

or points per correct answer. So, to calculate the number of points awarded per correct answer, we need to calculate the slope of the line.

Since the line passes through the points $(0,0)$ and $(3,6)$, we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1}\\[5pt] &=\dfrac{6-0}{3-0} \\[5pt] &= 2 \textrm{ points/correct answer} \end{align*}

So, each correct answer is worth $2$ points

To find the number of kilometers Jake rides per minute, notice that the units of the slope are

\[ \dfrac{\textrm{kilometers}}{\textrm{minute}}, \]

or kilometers per minute. So, to calculate the number of kilometers per minute, we need to calculate the slope of the line.

Since the line passes through the points $(0,0)$ and $(5,30)$, we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1}\\[5pt] &=\dfrac{30-0}{5-0} \\[5pt] &= 6 \textrm{ kilometers/minute} \end{align*}

So, Jake travels $6$ kilometers every minute

To find the number of liters consumed per mile, notice that the units of the slope are

\[ \dfrac{\textrm{liters}}{\textrm{mi}}, \]

or liters per mile. So, to calculate the number of liters consumed per mile, we need to calculate the slope of the line.

Since the line passes through the points $(0,60)$ and $(40,50)$, we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &=\dfrac{50-60}{40-0} \\[5pt] &= -0.25 \textrm{ liters/mi} \end{align*}

Notice that the result is negative because the number of liters is decreasing.

So, the car consumes $0.25$ liters of fuel per mile.

To find the number of tickets sold per day, notice that the units of the slope are

\[ \dfrac{\textrm{tickets}}{\textrm{day}}, \]

or tickets per day. So, to calculate the number of tickets sold per day, we need to calculate the slope of the line.

Since the line passes through the points $(0,100)$ and $(6,40),$ we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &=\dfrac{40-100}{6-0} \\[5pt] &= -10 \textrm{ tickets /day} \end{align*}

Notice that the result is negative because the number of tickets left available is decreasing.

So, $10$ tickets are sold each day.

The graph has a $y$-intercept at $(0,2),$ which means that the cost is $\$ 2.00$ even when no distance has been traveled. So, the company charges an initial fee of $\$ 2.00.$

To find the cost per kilometer, notice that the units of the slope are

\[ \dfrac{\textrm{dollars}}{\textrm{kilometers}}, \]

or dollars per kilometer. So, to calculate the cost per kilometer, we need to calculate the slope of the line.

Since the line passes through the points $(0,2)$ and $(2,3)$, we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &= \dfrac{3-2}{2-0}\\[5pt] &= \dfrac{1}{2} \\[5pt] &= 0.5\textrm{ dollars/kilometer} \end{align*}

So, the cost of a ride is $\$ 2.00$ plus $\$ 0.50$ per kilometer.

The graph has a $y$-intercept at $(0,3),$ which means that the cost on entering the parking lot is $\$ 3.00.$

To find the cost per hour, notice that the units of the slope are

\[ \dfrac{\textrm{dollars}}{\textrm{hours}}, \]

or dollars per hour. So, to calculate the cost per hour, we need to calculate the slope of the line.

Since the line passes through the points $(0,3)$ and $(4,6)$, we find its slope as follows: \begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &= \dfrac{6-3}{4-0}\\[5pt] &= \dfrac{3}{4} \\[5pt] &= 0.75\textrm{ dollars/hour} \end{align*}

So, the cost of parking is $\$ 3.00$ plus $\$ 0.75$ per hour.

To model the given situation, we will use the slope-intercept form \[ y=mx+b, \] where $y$ is the total cost, and $x$ is the time in hours. We fill in the information from the problem:

• The initial cost (when $x=0$) is $\$2.$ So, our graph will pass through the point $(0,2).$ This means that the $y$-intercept is $b=2.$

• After the initial fee, the cost of parking is $\$1$ per hour. So, the slope must be $m=1.$

Substituting the values from above, we get the equation \[ y=1x+2. \]

To graph this equation, we can pick two points and draw a line through them. One point can be the $y$-intercept $(0,2).$ We can find another point by substituting some $x$-value, say $x=2,$ into the equation:

\begin{align*} y&=1x+2 \\ y&=1(2)+2 \\ y&=4 \end{align*}

We plot the points $(0,2)$ and $(2,4)$ and draw a line through them:

To model the given situation, we will use the slope-intercept form \[ y=mx+b, \] where $y$ is the total cost, and $x$ is the distance in kilometers. We fill in the information from the problem:

• The initial cost (when $x=0$) is $\$4.$ So, our graph will pass through the point $(0,4).$ This means that the $y$-intercept is $b=4.$

• After the initial fee, the cost is $\$1$ per kilometer. So, the slope must be $m=1.$

Substituting the values from above, we get the equation \[ y=x+4. \]

To graph this equation, we can pick two points and draw a line through them. One point can be the $y$-intercept $(0,4).$ We can find another point by substituting some $x$-value, say $x=2,$ into the equation:

\begin{align*} y&=x+4 \\ y&=(2)+4 \\ y&=6 \end{align*}

We plot the points $(0,4)$ and $(2,6)$ and draw a line through them: