Question

lane wants to do a group scooter rental from boot scootin’ scooter company for her birthday party. using the information from the table, write an equation that best describes the relationship between the total cost and the number of minutes the scooter is rented.

of minutes cost

10 $56.50
20 $68.00
30 $79.50
equation: ____________
cost of renting for 33 minutes: ____________

Explanation:

Step1: Find the slope

The slope $m$ of a linear - equation $y = mx + b$ (where $y$ is the cost and $x$ is the number of minutes) is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(10,56.50)$ and $(x_2,y_2)=(20,68.00)$. Then $m=\frac{68.00 - 56.50}{20 - 10}=\frac{11.5}{10}=1.15$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Using the point $(10,56.50)$ and $m = 1.15$, we have $y-56.50 = 1.15(x - 10)$. Expanding gives $y-56.50=1.15x-11.5$. Then $y=1.15x + 45$.

Step3: Calculate the cost for 33 minutes

Substitute $x = 33$ into the equation $y=1.15x + 45$. So $y=1.15\times33+45=37.95 + 45=82.95$.

Answer:

Equation: $y = 1.15x+45$
Cost of renting for 33 minutes: $\$82.95$