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Monday, April 03, 2006

Somebody found my blog searching Google for this:

A graph has an x intercept of -3 and a y intercept of 3 Whats the slope?

I doubt he or she found anything to help in my stuff. If you come back again, here's how to find your answer.

One way to calculate slope is to take two points and divide the difference between the Y-coordinates by the difference between the X-coordinates. You have to start with the same point each time or you might get the signs confused.

An X intercept of -3 means you have a point at (-3,0). That's because where your line crosses the X axis, the Y coordinate has to be zero. Y intercept of 3 gives you a point at (0,3). So (3-0)/(0-(-3)) is 3/3, which is 1. Your slope is 1.

To use a different pair of points as an example, try (2,5) and (4,9). (9-5)/(4-2) = 4/2 = 2. You have a slope of 2. If you plot this, you will see that you have a much "steeper" slope than your problem above.

Another way to look at it is that your slope is "rise over run", that is, to go from one point to another, how far up do you have to go, divided by how far over to the right. If you have to go down and to the right, or up and to the left, your slope will be negative. If you are using intercepts, you're starting from zero, that is from the other axis, each time. So starting from an X intercept of -3 you have to go three units to the right to get to the Y-axis. And to get to the Y intercept of 3 you have to go up three units from the X-axis. The rise is 3, the run is 3, the slope is 1.

A line with a slope of 1 is always at a perfect 45 degree angle from your axes (providing that both axes are scaled the same), and goes from the lower left to the upper right. When X goes up, Y goes up. A slope of -1 means it goes from the upper left to the lower right. That is, when X goes up, Y goes down, and vice versa.

The best thing you can do is plot this yourself on a piece of paper. You don't even have to use graph paper - just scratch in an X and a Y axis and mark off some points. Do this a few times and you can get it in your head what that slope of 1 is really telling you. You will thank yourself later.

4 comments:

change destiny said...

I just wish all slopes were that simple .

Laura(southernxyl) said...

Oh, I know. If you could only go back to Algebra I, you could probably do it in your sleep.

F said...

Mommy, you always have to be everyone's mother, don't you?

Laura(southernxyl) said...

You're right! I can't help it! I think if I saw a rattlesnake struggling with its math homework I would pick up a pencil and say "let me show you"!