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Math Help - linear equations

  1. #1
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    linear equations

    The table shows the census data for New Hampshire since 1950.

    year pop

    1950 533242
    1960 606921
    1970 746284
    1980 920610
    1990 1113915
    2000 1238415

    1. Write an equation for the line that contains the data points for 1950 and 2000

    My answer is y= 14,103X + 533242

    I used ( 0, 533242 ) and ( 50, 1238415 ) to make an equation.

    2. Write an equation for the line that contains the the data points for
    1990 and 2000.

    I used ( 0, 1113915 ) ( 10, 1238415 )

    My answer is y = 112,450X + 1113915

    3. Use each of these equations to predict the population of New Hampshire in 2010. And for each prediction explain why you could expect it to provide an accurate forecast.

    y= 14,103X + 533242 1,379,422 ( I plugged in 60)


    y = 112,450X + 1113915 3,362,915 ( i plugged in 20)

    I think my first equation in correct but did I do something wrong with my
    second equation?

    Thanks.

    Vicky.
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  2. #2
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    are you sure the first equation is correct because when you plug in 50 it gives you 1238392 for the yr 2000 pop and not 1238415.

    and same with the second equation, it doesnt agree with the data when you plug in 10.

    (x,y) (x',y')

    the equation has gradient m=(y'-y)/(x'-x)

    then y=mx+c where c is a constant etermined by plugging in a value.

    ( 0, 1113915 ) ( 10, 1238415 )

    gradient is (1238415-1113915)/(10-0)=12450

    so y=12450x+c

    x=0 gives y=c=1113915

    so equation is y=12450x+1113915

    i think maybe you mistyped 12450 and wrote 112450 by accident.

    ( 0, 533242 ) and ( 50, 1238415 )

    y=(705173/50)x+533242

    y=14103.46x+533242

    now try them
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  3. #3
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    Quote Originally Posted by Vicky1997 View Post
    The table shows the census data for New Hampshire since 1950.

    year pop

    1950 533242
    1960 606921
    1970 746284
    1980 920610
    1990 1113915
    2000 1238415

    1. Write an equation for the line that contains the data points for 1950 and 2000

    My answer is y= 14,103X + 533242

    I used ( 0, 533242 ) and ( 50, 1238415 ) to make an equation.

    2. Write an equation for the line that contains the the data points for
    1990 and 2000.

    I used ( 0, 1113915 ) ( 10, 1238415 )

    My answer is y = 112,450X + 1113915 <<<<< you've got a nervous index finger. The equation of the line is: y = 12,450X + 1113915
    3. Use each of these equations to predict the population of New Hampshire in 2010. And for each prediction explain why you could expect it to provide an accurate forecast.

    y= 14,103X + 533242 1,379,422 ( I plugged in 60)


    y = 112,450X + 1113915 3,362,915 ( i plugged in 20)

    I think my first equation in correct but did I do something wrong with my
    second equation?

    Thanks.

    Vicky.
    ...
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  4. #4
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    I'll make sure I double check my calculations from next time.
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