A 5-mile cab ride costs $9.30. A 11-mile cab ride costs $17.70. Find a linear equation that models cost c as a function of distance d.

Treat the data as two ordered pairs (5,930) and (11,1770) of the form (d,c)

take the slope, then find the equation in the form
c = md + b ( just like y = mx + b)

To find a linear equation that models the cost c as a function of the distance d, we can use the two points given: (5, 9.30) and (11, 17.70).

The equation of a linear function is given by y = mx + b, where m is the slope and b is the y-intercept. In this case, c represents the cost, which is the y-value, and d represents the distance, which is the x-value.

First, let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Using the two points (5, 9.30) and (11, 17.70):

m = (17.70 - 9.30) / (11 - 5)
m = 8.40 / 6
m = 1.40

Now that we have the slope, let's substitute one of the points into the equation y = mx + b to solve for b (the y-intercept).

Using the point (5, 9.30):
9.30 = 1.40 * 5 + b
9.30 = 7 + b
b = 9.30 - 7
b = 2.30

Now, we have the values of m and b, so we can write the linear equation:

c = 1.40d + 2.30

Therefore, the linear equation that models the cost c as a function of the distance d is c = 1.40d + 2.30.