Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]
Step-by-step explanation:
Determine the equation form of the inequality
Given function form
Point-Slope form : y = mx + b
Given the information from the graph
Since the graph crosses (0, 2), b = 2
Find the slope
Choose any two points from the graph
(x₁, y₁) = (0, 2)
(x₂, y₂) = (2, 3)
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (3 - 2) / (2 - 0)
Slope = 1 / 2
m = 1 / 2
Therefore, the equation form of the inequality is y = (1/2)x + 2
Determine whether it is ≤ or ≥
Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.
The shaded region is below the solid line, therefore, it is ≤
Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]
To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.
y ≤ (1/2) x + 2
0 ≤ (1/2) 0 + 2
0 ≤ 2 TRUE
Hope this helps!! :)
Please let me know if you have any questions
