Question

Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?

Answer 1

The answer is B

Answer 2

y > -2x + 2

Explanation:

Notice that the section represented by the given inequality is that highlighted in black on the lower left of the graph.

The upper part of the graph must be an inequality that doesn't include the actual boundary line because such is represented with a dotted line instead of a solid one (so the equal sign must NOT be in the inequality).

The boundary line for the upper section has also the same slope as the one given (-2), and we also see that it goes through the value 2 on the y-axis, so such line in slope y-intercept form must be:
`y=-2x+2`

Since we need to include the (x,y) values on the plane that are "larger than" (y-value above) the boundary line we found, we need to select the "greater than" symbol for the inequality and :

y > -2x + 2