A 2-mi cab ride costs $1.70. A 7-mi cab ride costs $3.70. Find a linear equation that models cost c as a function of distance d.
a.
c = 0.53d + 0.90
b.
c = 0.85d + 2.00
c.
c = 0.40d + 0.90
d = 0.40c + 2.00
c = m d + b
1.7 = 2 m + b
3.7 = 7 m + b
===================
-2 = -5 m
m = 2/5
so
c = (2/5) d + b
1.7 = (2/5)2 + b
b = 1.7 - .8 = .9
so
c = (2/5) d + 9/10
or
10 c = 4 d + 9
To find a linear equation that models the cost c as a function of distance d, we can start by considering the information provided.
Given that a 2-mi cab ride costs $1.70 and a 7-mi cab ride costs $3.70, we can set up two equations based on this information.
Equation 1: 2d + b = 1.70
Equation 2: 7d + b = 3.70
To eliminate b, we can subtract Equation 1 from Equation 2:
7d + b - (2d + b) = 3.70 - 1.70
5d = 2
Now, we can solve for d:
d = 2 / 5
d = 0.4
Substituting this value back into Equation 1 or Equation 2, we can find the value of b:
2(d) + b = 1.70
2(0.4) + b = 1.70
0.8 + b = 1.70
b = 1.70 - 0.8
b = 0.90
So, the equation that models the cost c as a function of distance d is:
c = 0.40d + 0.90
Therefore, the answer is c. c = 0.40d + 0.90.