Question

A 5-mile cab ride costs $7.20. A 9-mile cab ride costs $11.60. Find a linear equation that models a relationship between cost c and distance d.

c = 1.44d + 4.40
d = 1.10c + 4.40
c = 1.29d + 1.70
c = 1.10d + 1.70

Answer 1

c - 7.2 = (11.6 - 7.2)/(9 - 4) (d - 5)
c - 7.2 = 4.4/4 (x - 5) = 1.1(d - 5)
c = 1.10d - 5.5 + 7.2
c = 1.10d + 1.70


The last option is correct.

Answer 2

Let

d--------> the distance in miles

c-------> the cost in dollars

`A(5,7.20)\\B(9,11.60)`

Step
`1`

Find the slope AB of the linear equation

we know that

the formula to calculate the slope between two points is equal to

`m=((c2-c1))/((d2-d1))`

substitute the values in the formula

`m=((11.60-7.20))/((9-5))`

`m=((4.40))/((4))`

`m=1.10`

Step
`2`

Find the equation of the line with m and the point A

`A(5,7.20)\\m=1.10`

we know that

the equation of the line in the point-slope form is equal to

`c-c1=m*(d-d1)`

substitute the values

`c-7.20=1.10*(d-5)`

`c=1.10d-5.50+7.20`

`c=1.10d+1.70`

therefore

the answer is the option

c = 1.10d + 1.70