Question

A taxi service charges a pick-up fee plus a charge for each mile driven. the equation y=1.8x+5 gives the total cost y to travel x miles in the taxi

Answer 1

Part A

The equation that gives the total cost, y to travel x miles is:

`y=1.8x+5`

When x=0

`\begin{gathered} y=1.8(0)+5=0+5 \\ y=5 \end{gathered}`

When x=10

`\begin{gathered} y=1.8(10)+5=18+5 \\ y=23 \end{gathered}`

When x=20

`\begin{gathered} y=1.8(20)+5=36+5 \\ y=41 \end{gathered}`

When x=30

`\begin{gathered} y=1.8(30)+5=54+5 \\ y=59 \end{gathered}`

When x=40

`\begin{gathered} y=1.8(40)+5=72+5 \\ y=77 \end{gathered}`

We can then fill the table using these values.

Part B

The y-intercept is the point at which x=0

From the table above, when x=0, y=5

• Therefore, the y-intercept is 5.

To use the table to find the slope, first, pick any two pair of points.

• For an example, I pick the points (0,5) and (10,23).

Then find the slope using the formula below:

`\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(23-5)/(10-0) \\ =(18)/(10) \\ m=1.8 \end{gathered}`