Question

The graph below represents which system of inequalities?

A) y ≤ −2x + 3
y ≤ x + 3
B) y ≥ −2x + 3
y ≥ x + 3
C) y ≤ −3x + 2
y ≤ −x + 2
D) y > −2x + 3
y > x + 3

Answer 1

A) y ≤ -2x+3; y ≤ x+3

Explanation:

The graphed lines are solid, and the shaded area is below both lines. This means the inequalities will be of the form y ≤ .... Only selections A and C have those comparison operators.

The lines both intersect the y-axis at y=3, so both equations will be of the form ...

... y ≤ ( )x + 3

Only selection A has that form.

_____

Check

The line with negative slope has a "rise" of -2 for a "run" of 1, so a slope of -2. Its equation is y = -2x +3.

The line with positive slope has a "rise" of 1 for a "run" of 1, so a slope of +1. Its equation is y = x + 3.

These equations tell you the desired inequalities are ...

• y ≤ -2x +3
• y ≤ x +3

matching selection A.