A taxi charges $1.75 plus a fee of $0.75 for each mile traveled. The total cost of a ride, without a tip, is $4.75. How many miles is the trip?

The trip contains 4 miles.

Step-by-step explanation:

The slope-intercept form of the line equation

where

Given that A taxi charges $1.75, meaning the initial condition of the trip is to charge $1.75.

Thus, y-intercept b = 1.75

Also, the taxi charges a fee of $0.75 for each mile traveled.

Thus, rate of change or slope m = 0.75

Let 'y' be the total cost

Let 'x' be the number of miles

Given that the total cost of a ride, without a tip, is $4.75.

so substitute y = 4.75, rate of change or slope m = 0.75, and the y-intercept b = 1.75 in the slope-intercept form of the line equation

y = mx + b

4.75 = 0.75(x) + 1.75

switch sides

0.75(x) + 1.75 = 4.75

subtract 1.75 from both sides

0.75x + 1.75 - 1.75 = 4.75 - 1.75

0.75x = 3

divide both sides by 0.75

0.75x/0.75 = 3/0.75

x = 4 miles

Therefore, the trip contains 4 miles.

x = 3 ± √(5+y)