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Step-by-step explanation:
<h2>Determine the equation form of the inequality</h2><u>Given function form</u>
Point-Slope form : y = mx + b
- m = slope
- b = y-intercept
<u>Given the information from the graph</u>
Since the graph crosses (0, 2), b = 2
<u>Find the slope</u>
<em>Choose any two points from the graph</em>
(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 <u>y = (1/2)x + 2</u>
<h2>Determine whether it is ≤ or ≥</h2>Since it is a <u>solid line</u>, 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<u> ≤</u>
Therefore, the inequality is
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!! :)
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