SOLUTION: 1.) when solving a linear inequality, why do you always solve for y? 2.) when graphing a linear inequality, how do you know if the inequality represents the area above or below

Algebra ->  Linear-equations -> SOLUTION: 1.) when solving a linear inequality, why do you always solve for y? 2.) when graphing a linear inequality, how do you know if the inequality represents the area above or below       Log On


   

Question 4776: 1.) when solving a linear inequality, why do you always solve for y?
2.) when graphing a linear inequality, how do you know if the inequality represents the area above or below the line?
3.) why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. always for y? in a linear system there is just 1 unknown and typically it is x --> you want to find where the line crosses the x-axis, this is where y=0.

2. you graph the equality --> the line, eg y=2x. Then if we want the region defined by y>2x or y<2x, if you cannot see this, just pick any point you like - not on the line, just a random point...how about (6,0).

If we put these into the equation y=2x, we get 0 and 12 ie 0<12 so, whichever half the pont (6,0) is in, this is y<2x, so y>2x is the other half.

Hope that has explained it well enough?

3. the straight line is the physical representation of the equation. That is why we draw graphs, because they are a visual insight into the line (or curve). As such, any point on the line (or curve) will satisfy the equation.

Hope this is all clear? They are very good questions to ask. I just hope i have answered them well enough - pictures are more helpful with this sort of question.

jon