Question

Which inequality will have a shaded area above its graph?

Answer 1

x − 9y ≤ 1

Because If you solve the equation y will be greater than ...

x − 9y ≤ 1 

Solve for y...

Subtract x from both sides...

- 9y ≤ - x + 1 

Divide both sides by -9 

REMEMBER WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER FLIP THE INEQUALITY SIGN....

y  ≥   x/9 - 1/9

Answer 2

To find the inequality whose graph is shaded *above* the line, you’ll have to find the inequality in which y is greater than the right side of the inequality. This boils down to isolating y in each of these, but there’s a bit of a shortcut you can take if you know about how multiplying/dividing both sides of an inequality by a negative number flips the inequality.

If the coefficient of y is negative, you’ll have to flip the inequality sign around in the process of isolating y. Which of those options have negative coefficients for y, and how would flipping the inequality sign effect them? Try to find the one option where the inequality ends up facing the y.