A Little Question on Graphing Linear Inequalities?

Question

I know the difference between a solid and dotted line (when graphing linear inequalities); in my text book it states that if the graph has a dotted line, the points on the line are NOT part of the solution of the inequality. My question is, if the line on the graph is solid; can the points on the line be a solution to the inequality?

Okay, thanks for answering! :) I just had to make double sure because I didn't want to mess up on all of my work over it. ^.~

Answer 1

Yes. If they were not a solution then they would not belong to the solution set nor the non-solution set, and they clearly must belong to one or the other - right?

Answer 2

Sure, if it's a greater than or equal to it includes the line.

The line represents equality, so it just depends on the nature of your inequality.

y ≤ mx+b is the line and the area underneath.

Btw, the way I find the area of the inequality it to put my pencil on the line and then see which way I'd have to move the pencil to maintain the inequality. For the above example I would see that y can be less than the y value of the line and so the area underneath is included.

Answer 3

The answer would be yes becuase it says the dotted line is not part of the inequality. Therefore,The solid line has to be the inequality because those are your only two choices.

Answer 4

for a million and a couple of you want to graph them, replace them to y=3x-6 and y=2-x. Then the position both lines bypass is the answer, in the journey that they bypass at (3,4) it extremely is one answer for substitution y=3, then positioned this into first one 3=5x-7 upload both equations? no longer confident? very last one, draw, yet use dotted lines, then colour above or lower than the line (i take advantage of wager and examine out to be sure which area)