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?
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 $\displaystyle x$ be how many miles apart the cities are
Let $\displaystyle y$ be the cost of the trip.
then for the first trip, we have $\displaystyle (x,y) = (260,90)$
and for the second trip, we have $\displaystyle (x,y) = (500, 150)$
Now let $\displaystyle (x_1,y_1) = (260, 90)$ and $\displaystyle (x_2,y_2) = (500,150)$
then the slope of the line connecting these two points is given by:
$\displaystyle m = \frac {y_2 - y_1}{x_2 - x_1}$
now, by the point slope form, we have the equation of the line given by:
$\displaystyle y - y_1 = m(x - x_1)$
plug in the values when you find $\displaystyle m$ and solve for $\displaystyle y$. after that, you have the relationship. to find how much a trip between cities 1000 miles apart costs, just plug in $\displaystyle x = 1000$ into the equation of the line and solve for $\displaystyle y$
try it