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Describe the steps you would follow in graphing x+2y<=2. Include in your answer whether you use a solid or broken line and where you shade, above or below the line.

2007-07-18 21:01:18 · 4 answers · asked by Anonymous in Science & Mathematics Mathematics

4 answers

Putting it into slope-intercept form, you get y<-1/2x+1
To graph, start at (0,1) and go up 1, left 2, that's your next point. From there, draw a DOTTED line through those two points ((0,1) and (-1,2)). It is DOTTED because it is not < with an equals sign beneath it. You shade below it because it is y< ...... To check that you indead shade below the dotted line, you can check the point (0,0) to see if it is shaded. It comes out to 0<2, which is right, so (0,0) is a solution to the equation, solidifying that the shaded region should be below the dotted line.

2007-07-18 21:08:22 · answer #1 · answered by yankeesrus07 2 · 0 0

First of all, since it can be equal to, it is a solid line no matter what.

For simplicity purposes, start of by imagining the < isn't there for now so the equation is x + 2y = 2. Now treat it like a normal equation (assuming you know how to solve equations with multiple variables). So x = 2-2y. Plug the solution for the equation I just did in to the original equation for x. So it would be:

(2-2y) + 2y= 2. Simplified it would be -2y + 2y = 2-2. Solve that and you get the equation 0 = 0. After completing all of those steps we re-incorporate the < sign. The equation would be 0 is less than or equal to (I said the words because the sign for it isn't on the keyboard) 0. In this situation, there are no variables in the final equation so it is fairly easy to graph.

The final equation is true because 0 is less than or equal to 0 and so the entire graph would be shaded (I'm not 100% sure about that last sentence but everything before it is definetely right).

2007-07-18 21:20:36 · answer #2 · answered by Justin G 2 · 0 0

2y < -x + 2
y < -x/2 + 1

The slope of the borderline is -1/2 and the y-intercept is 1. Thus you have a point at (0,1). Set y=0 in the equation to get the x intercept:

0 = -x/2 + 1
x = 2

The x-intercept is 2 so you have another point at (2,0).

Draw a dashed line through the two points and shade the area to the left of the line signifying <.

2007-07-18 21:13:47 · answer #3 · answered by gebobs 6 · 0 0

You can't. It's undefined. If it wasn't, then the graph would be a vertical line that intersected the x axis at -2.

2016-05-17 07:52:46 · answer #4 · answered by lavonia 3 · 0 0

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