How to Draw Linear Equations

Date: 06/07/99 at 23:05:46
From: V
Subject: How to draw linear equations

I have a lot of trouble drawing linear equations.

Under the y = mx+b formula, say I had y = (2/3)x + 5. How would I draw 
that? How would I go about finding other points?

Date: 06/07/99 at 23:27:13
From: Doctor Jeremiah
Subject: Re: How to draw linear equations

Hi there.

Getting a mental picture of what an equation looks like is not always 
easy. But there are clues to help us.

y = mx + b is used for straight lines, so anything that fits that 
equation is a straight line.

y = (2/3)x + 5

The value of b is the y-intercept, and because b = 5 the line crosses 
the y-axis at y = 5. So we will put a mark on our graph at 5 on the 
y-axis.

              |
              |
              |
              |
   (0,5) ==>  X
              |
              |
              |
              |
  ------------+-----------------
              |
              |
              |
              |

Then we notice that the slope is 2/3. Slope is measured in rise 
divided by run. Since the slope is 2 divided by 3 then each step is a 
rise of 2 and a length of 3. So the second point will be 2 above the 
first point and 3 over to the right.

              |
              |  (3,5+2) ==>  X
              |               |
              |            two up
              |               |
   (0,5) ==>  X --three over--
              |
              |
              |
              |
  ------------+-----------------
              |
              |
              |
              |

Now that we have two points we can take a ruler and draw a straight 
line that touches both points and the graph is done.

If the slope is negative then the rise will be less than zero. This 
means that the second point will be below the first point (but still 
to the right).

Let me know if you need more details.

- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/