If A = {(x, y)|x + 2y = 7}, is Set A a function?

Question

If A = {(x, y)|x + 2y = 7}, is Set A a function?

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Isabelle 2 days 2021-10-12T11:30:59+00:00 1 Answer 0

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    2021-10-12T11:32:31+00:00

    Answer: Yes it is a function

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    Here are some reasons why

    1. We can solve x+2y = 7 for y to get y = -0.5x+3.5; this equation is in slope intercept form y = mx+b. All equations in the form y = mx+b are linear and also a function.
    2. For any input x, there is exactly only one y value that pairs with it.
    3. The vertical line test can be used to effectively verify item #2 above. The idea is that it is impossible to draw a vertical line through more than one point on the graph. So it is said to pass the vertical line test.

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