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Math Help - Graph the two points to find another solution.

  1. #1
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    Graph the two points to find another solution.

    An equation and two ordered pairs are given. Show that each pair is a solution. Then use the graph of the two points to determine another solution.

    What I have so far:

    y=x-5 (4, -1) and (1, -4)

    for (4, -1):
    4y=-1x-5
    is the same as y=-1/4x-5

    for (1,-4)
    1y=-4x-5
    is the same as y=1/-4x-5


    I'm not entirely sure how I graph these, though. Could someone give me a hand?
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  2. #2
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    For y=x-5, you need to show that (4, -1) and (1, -4) are solutions. This means that if you plug the x- and y-coordinates in from each point into your line, you get a true statement. So first, consider (4,-1):

    Put x = 4, y = -1 into your equation - this means you have to REPLACE x with 4 and REPLACE y with -1. In your original post, you just put the 4 and -1 in front of the x and y. They take the place of x and y, i.e.:

    -1 = 4 - 5.

    This is obviously a true statement, as 4 - 5 does equal -1. Because you get a true statement, you know the point is a solution.

    Repeat this process for (1, -4).

    Now, carefully plot the two points, using graph paper, and connect the points with a straight line. EVERY point your straight line passes through is another solution. On your graph, look for a point that has integer x- and y-coordinates that your line passes through (in other words, where your line crosses an intersection on the graph paper). Use that point for another solution.

    Sorry I can't draw it, but if you plot the points and connect them, I think it'll be clearer.

    Hope this helps!
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