Which linear inequality models the graph of the solid line y=2/3x−3

Question

with a shaded region below the line?(1 point)
Responses

y≥23x−3
y greater-than-or-equal-to Start Fraction 2 over 3 End Fraction x minus 3

y<23x−3
y less than Start Fraction 2 over 3 End Fraction x minus 3

y>23x−3
y greater than Start Fraction 2 over 3 End Fraction x minus 3

y≤23x−3

Answer 1

The graph has a solid line represented by the equation \( y = \frac{2}{3}x - 3 \) and a shaded region below the line.

Since the line is solid, it indicates that the points on the line are included in the solution set, meaning we use "greater than or equal to" or "less than or equal to." Since the shaded region is below the line, we are looking for a "less than or equal to" inequality.

Therefore, the appropriate linear inequality that models this situation is:

\[ y \leq \frac{2}{3}x - 3 \]

So the correct response is:

y ≤ \( \frac{2}{3}x - 3 \)