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Math Help - Critical Thinking

  1. #1
    Junior Member wpcp15's Avatar
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    Question Critical Thinking

    This is so confunsing, can someone please help?

    A line passes through A(3,7) and B(-4,9). Find the value of a if C(a,1) is on the line.

    I thought it had something to do with finding the slope . . .
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  2. #2
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    Quote Originally Posted by wpcp15 View Post
    This is so confunsing, can someone please help?

    A line passes through A(3,7) and B(-4,9). Find the value of a if C(a,1) is on the line.

    I thought it had something to do with finding the slope . . .
    1)Find the equation of the line y=mx+b

    Now substitute x=a and y=1.

    You have an equation for "a" solve for it.
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  3. #3
    Junior Member wpcp15's Avatar
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    So m=-2/7 and y-int=-8

    1=-2/7a+8

    a=24.5

    Is this right?
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  4. #4
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    Quote Originally Posted by wpcp15 View Post
    This is so confunsing, can someone please help?

    A line passes through A(3,7) and B(-4,9). Find the value of a if C(a,1) is on the line.

    I thought it had something to do with finding the slope . . .
    Hello,

    if you have 2 separate points P_1(x_1 , y_1)~\text{and}~P_2(x_2 , y_2) which lay on a line then the equation of the line is:

    \frac{y - y_1}{x - x_1} = \underbrace{\frac{y_2 - y_1}{x_2 -x_1}}_{\text{slope of the line}} . this formula is called two-points-formula of a straight line.

    Plug in the coordinates of the points. Don't forget with your problem x = a and y = 1. You'll get:

    \frac{1 - 7}{a - 3} = \frac{9 - 7}{-4 - 3} . Solve for a:

    \frac{-6}{a-3} = \frac{2}{-7}~\Longrightarrow~42 = 2a - 6 ~\Longrightarrow~ 2a = 48 ~\Longrightarrow ~ \boxed{a = 24}
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  5. #5
    Senior Member DivideBy0's Avatar
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    Refreshing approach earboth, I usually go through the process of finding the full equation first.
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