1/10/11

Hey guys, it's Richard.

Mr. P announced we have a test on Friday so we should all study for that. We'll also be getting a review tomorrow so we can be prepared for Friday.  Tomorrow is ALSO Mr. Piatek's wifes Name Day. Happy Name Day to her!!

Today in class we learned the last lesson of Analytic Geometry which was Graphing Systems of Linear Inequalities. Also for homework, we got a worksheet for Graphing Systems of Linear Inequalities.

Here is one of the examples we did today in class.

a) x + y > 6
   2x - 2y < 4
We'll be treating this as (AND) which would be an INTERSECTION, which is one of the two possible graphs of systems of inequalities. The other would be a UNION (OR).

1) First, we should put the equations into y = mx + b form. So it would look like ...

y > -x + 6
Where the slope would be -1 and the y-intercept would be 6.

2x - 2y < 4
-2y < -2x + 4
y > x - 2
Where the slope would be 1 and the y-intercept would be -2.

2) Secondly, graph the two lines and since the > or < isn't equal to then the lines should be dotted lines.

3) Thirdly, pick points on either side of both lines and depending on which one is true or false, then the side which is true you must shade in. For example, in class today

We chose the points (0,0) for the equation x + y > 6. Plug them in and you get,
0 > 6 which says 0 is greater than 6 which is false, so the side that has the points (0,0) is not the side you want to shade in. We then picked the points (6,1) for the same equation. Plug them in and you get, 7>6 which is correct, 7 is greater than 6. So the side that that point is on, shade in that side!

4) Lastly, determine which area is the solution. The area which both sides are shaded in would be the solution.
In this case, it would be the green area.















Have a good day!