Graph the solution set for this inequality:
-6x - 3y greater than or equal to -18

9514 1404 393

Step-by-step explanation:

In this form, it is not difficult to find the intercepts. Eliminate the term that has a zero value, and divide by the coefficient in the other term.

Y-intercept:

  for x = 0, the equation is ...

  -3y = -18

  y = 6 . . . . . . divide by -3

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X-intercept:

  for y = 0, the equation is ...

  -6x = -18

  x = 3 . . . . . divide by -6

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Solid vs Dashed

The boundary of the shaded area is a solid line through these points. (It is solid because the symbol ≤ includes the "or equal to" case, meaning that points equal to those on the line are in the solution set.)

Above vs Below

The negative signs can make it a little tricky to figure out the shading. If we multiply the equation by -1, we get ...

  6x +3y ≥ 18 . . . . . note the reversal of the comparison symbol

Now, both x and y have positive coefficients. The solution form ...

  ky ≥ ( ) . . . . for positive k indicates shading above the line

  kx ≥ ( ) . . . . for positive k indicates shading to the right of the line

The boundary line has negative slope, so "above" and "to the right" are both on the same side of the line (a good check of the answer).