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How do you get an inequality like #2x+y>2# in #y=mx+b# form?

Answer 1

Here is your inequality: #2x + y > 2#

Subtract 2x from both sides to obtain: #y > -2x + 2#

I think you were hoping that this new form would help you to graph the inequality and shade it properly!

So, use the slope m = -2 and the y-intercept (0,2) to draw your line as usual. Make the line dotted or dashed, so the reader knows NOT to include points on that line as "solutions" to this problem.

Now, you need to decide where to "shade" the graph. That means, what points will satisfy the inequality? Take a test point like (0,0) and see if it is true: #0 > -2(0)+2#
#0 > 2# is FALSE. So, do NOT shade on the side of the line where (0,0) is located.

Watch what happens when I move the point to the other side of the line (I would call it above the line):

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Answer 2

Nathan Axel

To convert the inequality (2x + y > 2) into the form (y = mx + b):

Subtract (2x) from both sides to isolate (y).
This results in (y > -2x + 2), which is in the form (y = mx + b).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you get an inequality like #2x+y&gt;2# in #y=mx+b# form?

How do you get an inequality like #2x+y>2# in #y=mx+b# form?