Question 529780: How do I find the iniquality for a graph?
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! I suppose you were given a graph and asked for the inequality that it represents. If you know how to graph an inequality, doing the reverse job should not be too dificult. You could do the reverse of each step, in the same order as you would do when graphing.
Inequalities are expressions like
3x+2<15 or
3x-y>6
The looks of the graph depend on what your inequality looks like.
Inequalities with only one variable, like 3x+2<15 are graphed on a number line. There are different ways to do it depending on what your teacher prefers.
Inequalities with 2 variables, like 3x-y>6 are graphed as a painted or shaded region in the x-y coordinate plane. To begin, the corresponding equality is drawn as a dashed or full line. If the sign is < or >, a dashed line is used. If the sign involves an "equal or", then the line is a full, bold line.
For example, for 3x-y>6, the line representing 3x-y=6 is drawn as a dashed line first. It is the line that passes through (2,0) and (0,-6).
If you see a line that intersects the axes at x=5 (5,0) and at y=7 (0,7), you can write the equation for that line as 7x+5y=35 (with 35 = 5x7). You can see how that always works, with any numbers, if you just substitute. In the case of (2,0) and (0,-6), you would write the equation as -6x+2y=-12, and then you might recognize that it is equivalent to 3x-y=6, what you get by dividing verything by (-2).
If you have multiple choice for the answers, it's even easier; you just see if a couple of points in the line fit each choice.
When graphing, the next step is to figure out which side of the line is the colored or shaded one. You could pick a point, like (0,0) and see if it belongs to the solution. With x=0 and y=0, you get 3x-y=3(0)-0=0. Since it is not true that 0>6, the shaded or colored part should be the one that does not include the origin. You could follow that reasoning to pick an inequality when given a graph.
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