Write in Slope-Intercept Form

Date: 11/06/97 at 21:20:17
From: Richard H.
Subject: Help

Hello,

I don't know how to do this problem.

I need to write in slope-intercept form: x - y + 2 = 0  
I also need to sketch it.

Date: 11/12/97 at 21:31:55
From: Doctor Otavia
Subject: Re: Help

Hello! Slope-intercept form is great; it makes graphing much easier.  

Let's take a line, say, 6x - 2y - 4 = 0, and put it into slope-
intercept form. Slope-intercept form is when a line is in the form 
   
   y = mx + b

where m is the slope and b is the y-intercept.  

To get a line into that form, we just need to move terms around until 
it looks like that.  So we start with the equation in the form given:

   6x - 2y - 4 = 0

Now we move the x-term over to the other side, so it looks like

   -2y - 4 = -6x

We move the 4 over to the other side too, because remember, we want 
the y-term to be alone on one side.  Now our equation looks like

   -2y = -6x + 4

We're almost there. But if you look at the general equation of the 
slope-intecept form, the y term has a coefficient of 1, so we need to 
divide both sides by -2 to get that, so it will look like

   y = 3x - 2

The line is now in slope-intercept form. Now we need to graph it, 
and slope-intercept makes it much easier. We know that if a line 
looks like y = mx + b, then m is the slope and b is the y-intercept. 
In the case of the line we're using, the slope is 3 and the 
y-intercept is -2.  

The y-intercept is the place on the y-axis where the line intersects 
it. So, on your graph, plot the point (0, -2), because we know that it 
lies on the line.  

Slope can be defined many ways, but one way of thinking about it is in 
terms of rise/run. (If you think of a line in terms of a hill, then 
the bigger the slope, the steeper it is, so if you had a line with a 
slope of 25, that'd be pretty steep.) Rise/run means that the slope is 
a sort of ratio, and that, in the case of this line, 3, which can be 
expressed as 3/1, for every 3 units you go (or rise) up, you move 
over 1. Or you can go over 1 and up 3 because the order doesn't really 
matter. (If your slope were a fraction, then things would really be 
easy, because if it were say, 2/3, then you'd just go up 2 and over 3 
to find the next point.)  

The way this helps you graph it is that if you know one point already, 
(and we already found one), then you can find another point from it by 
using the slope. Just go up whatever the rise is and over the run, or 
in this case, up 3 units and over 1 unit. I'll show you going over and 
then up on the graph, because it looks clearer when typing.  The O 
denotes a point, and the axes are in increments of 1.

                            y
                          5 +
                            |
                          4 +     O (2, 4)
                            |     |
                          3 +     |
                            |     |
                          2 +     |
                            (1, 1)|
                          1 +  O---
                            |  |
   -+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-- x
                            |  |  2  3  4  5  6
                         -1 +  |
                            |  |
                         -2 O---
                            |
                         -3 +
                     
So you see, you get a step-ladder sort of look, and all those points 
are on the line. (0, -2), (1, 1), (2, 4) etc. You could also go the 
other way, meaning go down 3 units and over 1 to the left instead of 
the right. To draw the line, all you need to do is connect the points, 
and voila! you're done.  

If you have a negative slope, say -2/3, then instead of moving 2 steps 
up and 3 steps to the right, you'd move two steps up and 3 steps to 
the left, because there's a negative sign. Remember, lines with a 
negative slope always start in the top left-hand corner and go to the 
bottom right-hand corner, whereas lines with a positive slope start in 
the lower left-hand corner, and go to the top right-hand corner.

I hope this example helps you do your problem.  You can use the same 
method I used to put x - y + 2 = 0 into slope-intercept form and then 
graph it. Good luck!

-Doctor Otavia,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/