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

1. ## 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.

2. ## 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'.

3. ## Re: how do you sketch graph of f(x) = ax+b?

Originally Posted by pickslides
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?

4. ## Re: how do you sketch graph of f(x) = ax+b?

Originally Posted by Resilient
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 $\displaystyle b \neq 0$.

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