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Math Help - problem solving with linear functions

  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pinkmath135 View Post
    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
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    Smile

    thanks for the help but how do i find the cost of the trip between the two cities 1000 mi apart?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pinkmath135 View Post
    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
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