Question

The taxi ride in Detroit cost $11 for 2 miles and $18 for 4 miles. Let x be the number of miles and y be the total fare. A. Write an equation in slope intercept form that represents the situation. B. What is the initial fee? C. What is the price per mile? D. How much would it cost to take the same taxi for 10 miles?

Answer 1

Answer:

Step-by-step explanation:

The taxi ride in Detroit cost $11 for 2 miles and $18 for 4 miles.

Let x be the number of miles and y be the total fare.

Taking points (2, 11) and (4, 18), the slope of the graph is expressed as

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

y2 =18

y1 = 11

x2 = 4

x1 = 2

Slope, m = (18 - 11) / (4 - 2) = 7/2

A. Equation in slope intercept form is written as y = mx + c. Our equation becomes

y = 7x/2 + c

B. To determine the initial fee, let us first find the intercept, c of the equation. Using point (4, 18), it becomes

18 = 7×4/2 + c

18 = 14 + c

c = 18 - 14 = 4

Our equation becomes

y = 7x/2 + 4

The initial fee would be when x = 0. It becomes

y = 7 × 0/2 + 4

y = $4

C. The price per mile is the slope. Therefore,

The price per mile = 7/2 = $3.5

D. 10 miles would cost 10× 3.5 = $35