Question

Which system of inequalities represents the graph?

A) (y - 6 \leq -11x)

B) (y + 3x \geq -4)

C) (-2x + 3y > 15)

D) (y - 6 \leq -11x) and (y + 3x \geq -4)

Answer 1

The correct system of inequalities that represents the graph is option D) (y - 6 ≤ -11x) and (y + 3x ≥ -4). The overlapping region of the two lines represents the graph of the system of inequalities.

Step-by-step explanation:

The correct system of inequalities that represents the graph is option D) (y - 6 ≤ -11x) and (y + 3x ≥ -4).

This system of inequalities includes two separate inequalities that must both be true for a point to be included in the graph. The first inequality (y - 6 ≤ -11x) represents a line with a negative slope that passes through the point (0,6).

The second inequality (y + 3x ≥ -4) represents a line with a negative slope that intersects the y-axis at -4. The overlapping region of the two lines represents the graph of the system of inequalities.