Question 201136
Hello....

Your first equation you wrote as:  y = 3/5 - 4.

I'm pretty sure you meant to say:  y = 3/5x - 4.

Under that assumption, I will tell you this:

Your equation is in the slope/intercept form for an equation of a line.  That means that the equation follows this format:   y = mx + b.   When you have a line in that format, then you know that "m" represents the slope of the line and "b" represents the y intercept.

Let's take this a step at a time then.....

If you want to find your "y" intercept, you solve for "y" by making "x" equal to 0.

So..... y = 3/5x - 4
        y = 3/5(0) - 4
        y = 0      - 4
        y = -4

In other words, if "x" equals 0, then "y" equals -4.   Therefore, you just found the first point on your graph and that point is (0, -4).  Now what?

Well, you have to look at your slope.   Your slope, remember, is represented by "m" in your equation.  So let's look at that:

y =   mx + b
y = 3/5x - 4

What is "m" in the above?  Do you see that "m" is 3/5?  Therefore, your slope is 3/5.  

Do you know that slope is defined as RISE over RUN.  (I'm not sure how to write that in this space, but think of RISE over RUN as a fraction --- rise/run).

So your 3 is the RISE and the 5 is the RUN.  Three tells you to go UP three spaces from your point located at (0, -4) and then after you go up 3, you should go over 5 spaces.   

(If 3 had been NEGATIVE, you would have gone DOWN three spaces - watch out for positives and negatives).

Sooooo, now your graph has the point (0, -4)and the 2nd point that is 3 up and 5 over from (0, -4)   That new point is located at (5, -1).  If you just "connect the dots" you will have your graph of a line.

Your 2nd problem is:

4x - y = 2 

All you need to do is put this equation in the y = mx + b format.  In other words, solve for y.  Let's try it:

4x - y = 2

4x - 4x - y = 2 - 4x  (subtract 4x from both sides)
        - y = 2 - 4x  (see how we got rid of the 4x on the left side?)
          y = -2 + 4x (divide both sides by -1)

          y = 4x - 2  (rearrange the problem so that it is in the 
                       correct format)

Now, you can graph this as you did the above problem.  Do you see your "y" intercept?  Make x = 0 and solve for y.  That means your first point is:  

(0, -2)

What is your slope?  Well, "m" equals 4, which is the same as 4/1, so remembering that the slope is rise over run, we can see that we must "rise" 4 spaces up, and "run" 1 space over from the point (0, -2).  Then you just connect those two points on the graph and you'll have your line.

For your 3rd problem, you had to solve x = - 4.   Here's something to know:

When x equals a number, the line is VERTICAL on the graph.  The slope is UNDEFINED.

When y equals a number, the line is HORIZONTAL on the graph.  The slope is 0.

Sooooo, x = -4 means that you draw a straight and vertical line that thru -4 on your coordinate plane.

Your 4th problem is in the y = mx + b format, so you should be able to do that by now.  :-)  

I hope this helps you.  Good luck!