Answer:
B
Explanation:
First, we determine the equation of the line in the slope-intercept form: y=mx+b
From the graph:
• The y-intercept of the line, b = 3
Next, we determine the slope using any two points on the line.
We pick points (0,3) and (-2,2)
[tex]\text{Slope }=\frac{2-3}{-2-0}=\frac{-1}{-2}=\frac{1}{2}[/tex]
Therefore, the equation of the line of symmetry will be:
[tex]y=\frac{1}{2}x+3[/tex]
Next, we determine the inequality sign.
We use the origin(0,0) to test the required region.
[tex]\begin{gathered} \text{When x=0 and y=0} \\ y=\frac{1}{2}x+3 \\ 0\boxed{\square}3 \\ \end{gathered}[/tex]
Since 0 is less than 3, the inequality sign will be less than or equal to.
Note: We use less than or equal to because we have a thick line.
We therefore have:
[tex]y\leqslant\frac{1}{2}x+3[/tex]
The correct option is B.
