In a certain city the cost for a taxi ride for 20 miles is $13. for 30 miles the cost is $18. assuming the number of miles is x find the linear equation for the cost.

We need to write the linear equation that is satisfied by (20,13) and (30,18).
                             $18 - $13         $5
The slope is m = = = $0.50/mile
                              30 - 20            10

We need to find the y-intercept of this function.  To do that, start with the slope-intercept form   y = mx + b

and subst. the y and x values from one of the two given points.  Suppose we choose (20,$13):

$13 = ($0.50/mile)(20 miles) + b

Then $13 = $10 + b, and b = $3.

There's an up-front charge of $3 just to step into the taxi.

The equation in question is y = ($0.50/mile)x + $3.00           (answer)