Question

A bike rental company charges a rental fee plus a per hour cost. Based on the graph, which equation represents the situation?-0)A)y=5xB)y=2.50x + 5y=5x + 2.50D)y=2.50x

Answer 1

To solve the question,

Let the rental fee be represented by y

Let the hourly fee be represented by x

To get the equation of the situation which is a sum of the two fees.

From the graph, the rental fee (y) and hourly fee can be obtained by picking two points from the graph

If we select the first point (2,10) where time = 2 hours and cost = $10

Also selecting the second point (6,20) where time = 6 hours and cost = $20

The equation can be obtained by using the formula:

`\frac{y2_{}-y_1}{x2_{}-x_1}\text{ =}\frac{y-y_1}{x-x1_{}}`

From the above, y2 = 20, x2 = 6

y1 = 10, x1 = 2

Substituting into the formula, we will obtain:

`\frac{20\text{ - 10}}{6\text{ - 2}}=\frac{y\text{ - 10}}{x\text{ - 2}}`

`\begin{gathered} (10)/(4)\text{ = }\frac{y\text{ -10}}{x\text{ - 2}} \\ \\ \Rightarrow(5)/(2)=\frac{y\text{ -10}}{x\text{ - 2}} \end{gathered}`

The next step is to cross multiply

5 (x - 2) = 2 (y - 10)

Expanding

5x -10 = 2y -20

Re-arranging

2y = 5x - 10 + 20

2y = 5x + 10

Divide both sides by 2

`\begin{gathered} y\text{ =}(5x)/(2)\text{ + 5} \\ \\ y\text{ = 2.5x + 5} \end{gathered}`

Answer is y = 2.5x + 5