Question

a 3-mile cab ride costs $5.75. A 5-mile cab ride costs $8.25.
Part 1: Find a linear equation that models that costs c as a function of the distance d. (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 costs

(just need help showing work >.< I do mental math)

Answer 1

They give you 2 points in the information, you need to find the rate of change of miles vs cost

Answer 2

(x,y) = (3 , 5.75)
(x1,y1) = (5, 8.25)

Rte of change = (y - y1) / (x - x1)

Answer 3

Then use the equation point-slope form

y - y1 = Rate of change*(x - x1)

to get a equation for the line

Answer 4

hm... C= 1.25 + 2.00 or C = 1.25 d + 2 (cost of 10-mile ride = 14.50 I just need help with how to show work for my answer

Answer 5

the equation we find will be in the form

y - y1 = m(x-x1)

we need to first find m

Answer 6

using the two points from the equation, the ones i listed above

m = (8.25 - 5.75)/ (5-3)

Answer 7

so, the slope m = 2.5/2 = 1.25

Answer 8

oh okay ..

Answer 9

now from the two points again, (3, 5.75) and (5,8.25) and the slope found m = 1.25

form and equation in the form

y - y1 = m*(x-x1)

Where x1 and y1 are from one of the points in the problem, either one is fine to use

Answer 10

oh I understand now c: thanks

Answer 11

what do you get

Answer 12

how you got 1.25 from the points

Answer 13

y - 5.75 = 1.25(x - 3)

y - 5.75 = 1.25x - 3.75

y = 1.25x + 2

Let c = y = cost , and x = miles = d

c(d) = 1.25*d + 2

Answer 14

1.25 is the rate of change of distance per mile , using the 2 points given
(x,y) = (3 , 5.75)
(x1,y1) = (5, 8.25)

Rate of change = (y - y1) / (x - x1) = (8.25 - 5.75) / (5 - 3) = 1.25

Answer 15

Now that you have the equation of the cost per distance

c(d) = 1.25d + 2

You can use that to find the cost of a 10 mile ride, Let d = 10 and find c(10) = ...

Answer 16

$14.50

Answer 17

yep, c(10 ) = 1.25*10 + 2 = 14.50

Answer 18

thanks so much c: