Question

Which linear inequality is represented by the graph?

A.y ≤ 2x + 4
B.y ≤ 1/2x + 3
C.y ≥ 1/2x + 3
D.y ≥ 2x + 3​

Answer 1

B. y ≤ 1/2x + 3

Explanation:

To write the equation of the inequality, use the linear equation form y = mx + b. The y-intercept is b and is where the line intersects the y-axis. Here b = 3. You can find the slope m by counting between points the vertical and horizontal distances. Here it is 1/2. Substitute m = 1/2 and b = 3.

y = 1/2x + 3

Since this is an inequality and a solid line has been used, you must use ≤ and ≥. To determine which is for this equation, test the point (0,0) in each.

y ≤ 1/2x + 3 y ≥ 1/2x + 3

0 ≤ 1/2(0) + 3 0 ≥ 1/2(0) + 3

0 ≤ 3 True 0 ≥ 3 False

Since (0,0) is a part of the set of solutions, the equation which is true is the correct equation.