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I am struggling with a problem. I need to graph 6x + 3y > 18 on a typical 10 number graph. Can you help me?

I cannot see how to graph 6x+3y>18. I think I shade everything over (0,0) but I can't get to that part because I can't figure the first part out despite looking at the book. I would appreciate any help.

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2 Answers

Hello, Valerie -- 

First you need to find the x-intercept and the y-intercept. Divide all the way through by 3 to reduce the inequality to an equivalent form:

       2x + y > 6

To find the y-intercept, let x = 0, and change > to =:

         2(0) + y = 6

             y-intercept is (0,6)

For the x-intercept, let y = 0:

          2x + (0) = 6

             x-intercept is (3,0)

Put those points on your graph and draw a dotted line through them (dotted because of the > inequality).

To finish the graph shade either above or below the dotted line. To determine the shaded area, pick a "test point" -- say (0,0) -- and substitute those values into the original. See whethere the result is true or false.

           6(0) + 3(0) > 9

This is false, because 0 < 9. You know now that the point (0,0) is NOT in the shaded area. It is below the dotted line, your shading must be above the line.

You could check another point -- say (3,2) to make sure. That point is above the line,making the inequality true,  so it will be in the shaded area.


I-   Solve for y:        3y > -6x + 18

                               y > -2x + 6

II -  Draw the boundary line:  y = -2x + 6 

      (Since y is greater than, and not equal to, -2x + 6, this is a dotted line)

III - Test any point away of the line to determine the shaded region.  For instance, if you test (0, 0), you will get the false statement:  0 > 0 + 6.  Since (0, 0) is located in the region below the boundary line, then the shaded region must be above the line.

Let me know if you need additional help with this.