Hi, so I have a series of equations that I need to be in Slope Intercept Form (y=mx+b) in order to graph, and I know how to graph them after they are in that form but I have trouble getting y by itself. Well actually instead of = it will be inequality signs but that shouldn't matter.
1.)
-x + 7y > 16
11x - y ≤ 12
2.)
2x + 5y ≤ 6
5x - 3y ≥ 9
3.)
3y < x/3 - 1
2y ≤ 2x + 1
4.)
3x ≥ 5y - 4
-2y < 4x - 1
(also i couldn't find the less than or equal to or greater to or equal to symbols on here so i looked online, you can just copy and paste mine from up there)
I'm sorry if this is a lot of problems, but it'll really help a lot!!
Example #4
-2y < 4x -1
Divide by -2 each side.....note if you divide or multiply by a negative you must reverse the < > symbol
y > -2x + 1/2
3x >= 5y - 4 add 4 to ea side
3x +4 >= 5y divide both sides by 5
3/5 x + 4/5 >= y or y <= 3/5 x + 4/5
+128707 These problems will produce solution "areas" [ if there are any]
1.)
-x + 7y > 16 add x to both sides → 7y > 16 + x divide both sides by 7 → y > [ 16 + x]/ 7
11x - y ≤ 12 add y to both sides, subtract 12 from both sides → 11x - 12 ≤ y rewrite as
→ y ≥ 11x - 12
Here is the graph of both areas......the "overlap" is the solution region...https://www.desmos.com/calculator/gf4lgz6brj
+128707 2.)
2x + 5y ≤ 6 subtract 5y, 6 from both sides
2x - 6 ≤ -5y divide both sides by -5 and reverse the inequality sign
(-2/5)x + (6/5) ≥ y
Rewrite as
y ≤ (-2/5)x + (6/5)
5x - 3y≥ 9 add 3y to both sides, subtract 9 from both sides
5x - 9 ≥ 3y divide both sides by 3
(5/3)x - 3 ≥ y rewrite as
y ≤ (5/3)x - 3
Here's the graph of this solution area.....https://www.desmos.com/calculator/bczrubgbac
