Question

Use the image to answer the question.

Four points and two intersecting lines are plotted on a coordinate plane. The x-axis ranges from negative 15 to 5 in unit increments, labeled at every 5 units. The y-axis ranges from negative 5 to 10 in unit increments, labeled at every 5 units.

Which point on the graph is a solution to the simultaneous inequalities y≤13x+2
and y<23x+4
?

(1 point)
Responses

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−10,−2)
left parenthesis negative 10 comma negative 2 right parenthesis

(−6,0)
left parenthesis negative 6 comma 0 right parenthesis

(2,5)

Answer 1

(-4, −2)

Check: y = −2. For y ≤ (1/3)x + 2: (1/3)(−4)+2 = −4/3+2 = 2/3, and −2 ≤ 2/3 (true). For y < (2/3)x + 4: (2/3)(−4)+4 = −8/3+4 = 4/3, and −2 < 4/3 (true). The other points fail one of the inequalities.