Question 201136: Graph each equation or inequality
1. y = 3/5 - 4
2. 4x - y =2
3. x = -4
4. y = 2x - 5
5. f(x) = 3x - 1
6. f(x) = [[3x]] = 3
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! 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!
|
|
|
