Let's make an equation 
No matter how far you go you have to pay a flat rate of $1.75
Every mile is an additional $0.65.
y= mx +b is the equation for a line. The rate at which the fee increase is linear because it always changes by a constant amount. So we can rewrite the problem as an equation.
y = 0.65x + b Well what can b be? b in the equation represents the y-intercept so we can say that it is the starting value because it is when x = 0. Or when the distance traveled is 0. What is the fee for just getting in the
taxi? $1.75. So then b = 1.75
y = 0.65x + 1.75 Where y is the cost of the ride and x is the miles traveled
So Katie only has $10. Let's plug that in for y and solve for x.
10 = 0.65x + 1.75
10- 1.75 = 0.65x
(10-1.75)/ 0.65 = x
(10-1.75)/.65 = 12.6923076923076923 miles or about 12.69 miles
