# Thread: problem solving with linear functions

1. ## problem solving with linear functions

Allied Airlines charges $90 for a ticket to fly between two cities 260 mi apart and$150 for a ticket to fly between to cities 500 mi apart. At this rate, what
would it cost for a trip between two cities 1000 mi apart?

2. Originally Posted by pinkmath135
Allied Airlines charges $90 for a ticket to fly between two cities 260 mi apart and$150 for a ticket to fly between to cities 500 mi apart. At this rate, what
would it cost for a trip between two cities 1000 mi apart?
use coordinates to fit a line through the two relations.

Let $x$ be how many miles apart the cities are
Let $y$ be the cost of the trip.

then for the first trip, we have $(x,y) = (260,90)$

and for the second trip, we have $(x,y) = (500, 150)$

Now let $(x_1,y_1) = (260, 90)$ and $(x_2,y_2) = (500,150)$

then the slope of the line connecting these two points is given by:

$m = \frac {y_2 - y_1}{x_2 - x_1}$

now, by the point slope form, we have the equation of the line given by:

$y - y_1 = m(x - x_1)$

plug in the values when you find $m$ and solve for $y$. after that, you have the relationship. to find how much a trip between cities 1000 miles apart costs, just plug in $x = 1000$ into the equation of the line and solve for $y$

try it

3. thanks for the help but how do i find the cost of the trip between the two cities 1000 mi apart?

4. Originally Posted by pinkmath135
thanks for the help but how do i find the cost of the trip between the two cities 1000 mi apart?
did you find the equation of the line? as i said, once you have the equation, plug in x = 1000 and solve for y, it will give you the cost for the 1000 mile trip