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

B. y ≤ 1/2x + 3

Step-by-step 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.