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Ceia Exum · May 13, 2009, 01:31 PM

I need help with inequalities, slopes, & linear lines.
Please refresh my memory. I need serious help. End Of Grade Testing is coming soon.

Perito · May 13, 2009, 02:29 PM

On your other post, I showed you that the equation for a line is Y=mX + b. You should memorize that!

If the slope is 0 (m=0), the line is simply Y=b and is horizontal. A vertical line is not a function of Y. It's something like X=17 (see, no Y!)

If the slope is not zero, they for any value of X, you can calculate a value of Y. For example here's a line, Y=3X+7. If X=1 then Y=10. If X=2 then Y=13. Here's a special case: if X=0, Y=7. That's why "b" is the "Y-intercept". It's the value of "X" when X=0. It's the place where the line crosses the Y-axis (and where the value of X is zero).

The slope is the change in Y divided by the change in X when going from any two points.

$Y_1=mX_1+b$

$Y_2=mX_2+b$

$slope\,=\,\frac {Y_2-Y_1}{X_2-X_1}=\frac {(mX_2+b) -(mX_1+b) }{X_2-X_1} = \frac {m(X_2-X_1)}{X_2-X_1}=m$

That's why they call it the slope.

There's not much more to it than that. You just have to think clearly.

As for inequalities, they're just like regular equations unless you multiply or divide by a negative number. Also, remember that if you have an equation like "Y < mX + b" or "y > mX + b", you can graph the line but the inequality lies on one side of the line or the other. The line, itself, is not included.

If the equation had been $Y \le mX+b$ or $y \geq mX+b$ , the values that fulfill the inequality would include the line.