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

• Jun 14th 2011, 04:40 PM
Resilient
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.
• Jun 14th 2011, 04:44 PM
pickslides
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'.
• Jun 14th 2011, 04:51 PM
Resilient
Re: how do you sketch graph of f(x) = ax+b?
Quote:

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?
• Jun 14th 2011, 06:16 PM
mr fantastic
Re: how do you sketch graph of f(x) = ax+b?
Quote:

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 $b \neq 0$.

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