Expert: Wei Chong - 7/8/2008

Question
given the function f(x)=1/3x
find the slope and the y intercept of the line
graph the equation, it's going to be hard to graph it on here, but you can tell me which direction (left to rigt heading up or passing through whatever points)

here's what I think. I believe the slope is 1/3 and the y intercept is 0, but i really don't know!

Answer
Hi Mel,

You are right. For f(x) = (1/3)x, the slope is 1/3 and the y-intercept is 0. It is important to understand the reason behind so you won't have any doubt.

The following link will explain why in detail (scroll down the page to watch the animated math video)

Slope-Intercept Form:
http://www.mathexpression.com/slope-intercept-form.html


Here's a quick explanation. An equation of a line can be written in slope-intercept form:

y = mx + c  ---- (1)

Where m = slope and c = y-intercept. Note that f(x) is the same as y.

What you have is:

 f(x) = (1/3)x  
=>f(x) = (1/3)x + 0  ---(2)

Comparing (1) with (2):

(1) y = mx + c
(2) f(x) = (1/3)x + 0

Clearly m = 1/3 and c = 0.

As to graphing it, you can learn the basics in this lesson:

Slope-Intercept Form Examples (shows example on how to graph)

http://www.mathexpression.com/slope-intercept.html

The graph for f(x) =(1/3)x + 0 will be a line passing through the origin (0,0) and will slant upwards to the right ( / ).


Best Regards,
Wei Chong