A 3-mi cab ride costs $4.50. A 7-min cab ride costs $8.10. Find a linear equation that models cost c as a function of distance d.
To find a linear equation that models the cost c as a function of distance d, we need to use the given information about the cost of cab rides for different distances.
Let's assign variables to represent the distance and the cost. We can let d represent the distance in miles and c represent the cost in dollars.
From the given information, we have two data points:
1) A 3-mile cab ride costs $4.50
2) A 7-mile cab ride costs $8.10
We can create two equations based on these data points:
Equation 1: 3m + b = 4.50
Equation 2: 7m + b = 8.10
Next, we can solve this system of equations to determine the values of m and b, which represent the slope and y-intercept, respectively, of the linear equation.
Subtracting Equation 1 from Equation 2 will eliminate the b term:
(7m + b) - (3m + b) = 8.10 - 4.50
4m = 3.60
m = 0.90
Now that we have the value of m, we can substitute it back into either Equation 1 or Equation 2 to solve for b:
3(0.90) + b = 4.50
2.70 + b = 4.50
b = 1.80
Therefore, the linear equation that models the cost c as a function of distance d is:
c = 0.90d + 1.80