Answer:
y ≥ -(1/3)x + 2
Step-by-step explanation:
First, we can identify the type of inequality present. We can notice two things about the graph:
- the shading is above, so the inequality is greater than the y-value of the boundary line
- the boundary line is solid (i.e. not dotted), so the inequality includes the boundary's y-value
From these observations, we can determine that the correct sign will be greater than or equal to: [tex]\ge[/tex].
Next, we can find the equation of the boundary line in slope-intercept form. We can see that its slope is:
slope = rise / run
slope = -1 / 3
slope = -1/3
And, the line's y-intercept is at:
y = 2
So, the equation of the boundary line is:
y = mx + b
y = -(1/3)x + 2
Hence, the inequality is:
y ≥ -(1/3)x + 2
