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Math Help - how do you sketch graph of f(x) = ax+b?

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    how do you sketch graph of f(x) = ax+b?

    how do you sketch f(x) = ax+b? i know how to sketch when a and b are given numbers, but I'm not sure what to do now as a and b could be any numbers and so the graph could literally look like any line. thankz.
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    Re: how do you sketch graph of f(x) = ax+b?

    It could look like anything, but you should know that 'b' is the y-intercept and 'a' gives the direction of the line.

    Therefore sketching y=ax+b for any 'a' and 'b', simply mark 'b' on the y-intercept and draw a line through it in the direction given by 'a'.
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    Re: how do you sketch graph of f(x) = ax+b?

    Quote Originally Posted by pickslides View Post
    Therefore sketching y=ax+b for any 'a' and 'b', simply mark 'b' on the y-intercept and draw a line through it in the direction given by 'a'.
    so it doesn't matter whether i chose negative b or positive, and the same for a, as long as i give the direction?
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    Re: how do you sketch graph of f(x) = ax+b?

    Quote Originally Posted by Resilient View Post
    how do you sketch f(x) = ax+b? i know how to sketch when a and b are given numbers, but I'm not sure what to do now as a and b could be any numbers and so the graph could literally look like any line. thankz.
    I'd break it up into a number of cases and sketch an example of each:

    Case 1a: a > 0 and b > 0.

    Case 1b: a > 0 and b = 0.

    Case 1c: a > 0 and b < 0


    Case 2a: a < 0 and b > 0.

    Case 2b: a < 0 and b = 0.

    Case 2c: a < 0 and b < 0.

    Case 3a: a = 0 and b \neq 0.

    Case 3b: a = 0 and b = 0.
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