Question

Which linear inequality is represented by the graph

Answer 1

Answer:$\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }$

Step-by-step explanation:

Determine the equation form of the inequality

Given function form

Point-Slope form : y = mx + b

• m = slope
• b = y-intercept

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 $\Large\boxed{y\leq \frac{1}{2}x+2 }$

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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