SOLUTION: A taxi cab charged $17.50 for a ten mile trip and $30 for a 20 mile trip. Write an equation to find the charge per mile and the cost just to get in the cab.

Question 1037913: A taxi cab charged $17.50 for a ten mile trip and $30 for a 20 mile trip. Write an equation to find the charge per mile and the cost just to get in the cab.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this would be a straight line equation.
the slope intercept form of a straight line equation is:
y = mx + b
m is the slope
b is the y-intercept.

let x = the number of miles.
let y = the cost for that number of miles.

you have 2 points.

(x1,y1) = (10,17.50)
(x2,y2) = (20,30)

the slope of a straight line equation is equalt to (y2-y1)/(x2-x1)

that would be (30-17.50)/(20-10)

simplify that to get slope = 12.50/10 = 1.25

your equation of y = mx + b becomes y = 1.25*x + b

now use one of the points to solve for b.

you replace x with the x-coordinate of one of the points and you replace y with the y-coordinate of that same point and then solve for b.

y = 1.25x + b becomes 30 = 1.25*20 + b when you use the point (20,30).

solve for b to get b = 30 - 1.25*20.

simplify to get b = 30 - 25.

combine like terms to get b = 5.

your equation is y = 1.25*x+5

what this equation says is that you will pay 5 dollars to get into the cab and then you will pay 1 dollar and 25 cents for each mile that the cab takes you.

for example:

to go 10 miles, the cost is 5 dollars plus 1.25 * 10 = 5 dollars + 12.5 = 17 dollars and 50 cents.

to go 20 miles, the cost is 5 dollars plus 1.25 * 20 = 5 dollars plus 25 dollars = 30 dollars.

the graph shows that to you.
x represents the number of miles.
y represents the cost to go that number of miles.

the graph is shown below:

$$$

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