Question

A 3-mile cab ride costs $5.75. A 5-mile cab ride costs $8.25.
Part1: Find a linear equation that models the cost c as a function of the distance d. (Hint: Create a table with data points and use the data from the table to write the equation.)
Part 2: How much will a 10-mile cab ride cost?

Answer 1

@Michele_Laino

Answer 2

so let's make some points. 3 miles costs $5.75, so (3, 5.75). 5 miles is $8.25 so (5, 8.25) now we can find the slope
\[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 3

How would you figure out what it cost for each mile?

Answer 4

that's what the slope is

Answer 5

\[\frac{ 8.25-5.75 }{ 5-3 }\]

Answer 6

please note that, using your data and conjecturing a linear relationship, namely if I caal with c the cost and with x number of miles, then I conjecture this:
c=a*x+b

Answer 7

\[\frac{ 2.50 }{ 2 }\]

Answer 8

inserting your numerical data, I can write:
\[5.75=3a+b\]
\[8.75=5a+b\]
solving those above equation in order to find a and b, we have:
a=1.25, and b=4.00

Answer 9

so the function c, is, please continue, namely insert values for a and b into the above equation

Answer 10

So the equation would be C = 1.25d + 4.00 ?

Answer 11

that's right!

Answer 12

On the answer key it says: C = 1.25d + 2.00

Answer 13

I was trying to figure out how the answer would be C = 1.25d + 2.00

Answer 14

2.5/2 is 1.25, so that's the slope. once we put that and one of the points, we put it in point-slope form to get y - 5.75 = 1.25(x - 3)

Answer 15

@Answers101 please note that it has been necessary to conjecture a linear relationship between number of miles and cost

Answer 16

once we convert it, we get y - 1.25x + 2

Answer 17

y =*

Answer 18

So the answer is C = 1.25d + 2.00 because we had to convert the linear relationship between the number of miles & the cost. ?

Answer 19

@Answers101 sorry you are right:
c=1.25 x+2.00

Answer 20

@Answers101 please substitute x=10, and then you will get your answer