Question

you are on vacation in new York city, and you need to get around town to different locations. below are the rates for 2 different cab companies, locally dubbed "the red cabs" and "the green cabs questions -1 - what is the cost to get into a green cab ?2 - how much does it cost per mile for a green cab ?3 - what is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a green cab? 4 - if you will be traveling 2 miles, which company should call and how much will it cost you ?5 - if you will be traveling 6 miles which cab company should you call and how much will it cost you 6 - how many miles would you travel for the cost to be the same for both cabs and how much will that cost you ? 7 - what is the difference in cost between the two companies if you need to travel 8 miles ?

Answer 1

The graph provided gives us the information for both cab companies, with the miles covered on the x-axis, and the cost per mile on the y-axis.

(1) The cost to get into a green cab is derived as follows;

$\begin{gathered} \text{The slope of the line is; } \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where: }(x_1,y_1)=(1,6) \\ (x_2,y_2)=(2,7) \\ m=\frac{7-6}{2-1} \\ m=\frac{1}{1}\Rightarrow m=1 \\ We\text{ shall use the slope-intercept form and the equation of the line is;} \\ y=mx+b \\ 6=1(1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}$

The cost to get into a green cab is $5 (that is the y-intercept)

(2) How much does it cost per mile for a green cab

$\begin{gathered} \text{Note that the slope as calculated above is 1} \\ \text{This means, it will cost \ 1 per mile for a green cab} \end{gathered}$

The cost per mile for a green cab is $1

(3) What is the equation in slope-intercept form, that relates the cost compared to the miles traveled for a green cab

The equation from the slope and y-intercept derived above is;

$\begin{gathered} m=1,b=5 \\ y=mx+b \\ y=(1)x+5 \\ y=x+5 \end{gathered}$

(4) If you are travelling 2 miles, which company should you call and how much would it cost you?

At 2 miles, the red cab would cost you $6, while the green cab would cost you $7. Therefore you should call the red cab company

(5) If you will be travelling 6 miles, which cab company should you call and how much would it cost you?

At 6 miles, the green cab would cost $11, while the red cab would cost $14. Therefore you should call the green cab company

(6) How many miles would you travel for the cost to be the same for both cabs, and how much would that cost you?

The graphs for both cab companies intersect at 3 miles/$8. This means, if you travel for 3 miles, either company would be charging you the same and that is $8.

(7) If you need to travel 8 miles, as shown on the graphs, the green cab would charge you $13, while the red cab would charge you $18. This means the difference in cost at 8 miles is $18 minus $13 and thats $5.