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Ceia Exum · May 13, 2009, 01:27 PM

please show me a step by step procedure.
find the slope of the line y=2/5x+6
Solve: 5(x+4)<-4+5x
find the slope passing through the points A(-5,-5) and B(6,1)
Solve: x+2-2(x+8)>0

Perito · May 13, 2009, 02:15 PM

1. find the slope of the line y=2/5x+6
2. Solve: 5(x+4)<-4+5x
3. find the slope passing through the points A(-5,-5) and B(6,1)
4. Solve: x+2-2(x+8)>0[/math]

1. The general form of a line is "y=mx+b". Where m and b are constants, not variables.
When you see an equation like this, the value of "m" is always the slope. The value of "b" is the "y-intercept" (or some people just say the "intercept".

Therefore, the answer to equation 1 is simply "2/5".

2.
$5(x+4)<-4+5x$ -- Are you sure this is correct?

$5x+20<4+5x$

$5x+20-20-5x < 4+5x-20-5x$

$0 < -16$ -- which is impossible. Therefore, there is no solution.

3.
The slope of a line is given by

$Slope = \frac {\Delta\,y}{\Delta\,x}$

where "Δ" means the "change in"

You have two points, (-5,-5), and (6,1)

$\Delta\,y = 6-(-5)=11$

$\Delta\,x = 1-(-5)=6$

$slope=\frac {\Delta\,y}{\Delta\,x}=\frac {11}{6}=1\, \frac 56$

4.
x+2-2(x+8)>0
x+2-2x-16>0
-14-x>0
x<-14

You can add and subtract from both wides without changing > to < or < to >. However, if you multiply or divide, you have to be sure that you aren't using a negative number. Sometimes that's hard to do. If you do use a negative number, you change the sense. Here's an example

$1 < 7$

multiply both sides by -1 (or any negative number), the sense changes:

$-1 \, \times \, 1 \, >\, -1 \, \times \, 7$

$-1 > -7$