Question

Help?!?! This is soo confusing!!

When you are graphing an inequality how do you know which part of the graph to shade in? And how do you determine if the line is solid or dotted?

Answer 1

Let's say we want to graph y < 3x+5

Answer 2

the "less than" sign means we shade below the boundary line

the boundary line itself is dotted/dashed because we are NOT including the boundary

Answer 3

if we flip the "less than" sign to a "greater than" sign, then we shade above the boundary line

the boundary line is only solid if you have "or equal to" attached to the inequality sign

Answer 4

oh and I nearly forgot, but the boundary line is simply the graph of y = 3x+5 (in this example)

Answer 5

Ok so if the inequality sign had a line under it meaning less than or equal to you would have a solid line

Answer 6

correct because that means to include the boundary in the solution set

Answer 7

this only works if y is completely isolated

Answer 8

Okay so what if you have like x+3y<4 or something? and y isnt by itself

Answer 9

we have to solve for y first

x+3y<4

3y<4-x

3y < -x + 4

y < (-1/3)x + 4/3

Answer 10

in this case, the inequality sign didn't flip, but it will flip when you divide both sides by a negative number

example: -2y > 5 turns into y < -5/2

Answer 11

Ohh okay so you would have to solve for y first that graph..makes sense
And the sign ONLY flips for negative numbers?

Answer 12

then*

Answer 13

yes when you multiply or divide both sides by a negative number

Answer 14

Ok thank you soo much!

Answer 15

you're welcome