Answer: Choice B. [tex]y \le -\frac{1}{3}x+1[/tex]
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Explanation:
We need to know the equation of the boundary line. This boundary goes through (0,1) and (3,0). Find the slope of the line through these points
m = (y2-y1)/(x2-x1)
m = (0-1)/(3-0)
m = -1/3, negative slope means the line goes downhill as we move from left to right.
The y intercept is b = 1 as this is where the boundary crosses through the y axis
y = mx+b turns into y = (-1/3)x+1 after replacing m and b with m = -1/3 and b = 1 respectively.
The equation of the boundary line is y = (-1/3)x+1
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The shading is below the boundary, so we'll have a "less than" sign involved here. More specifically, we'll have a "less than or equal to" sign because the boundary is a solid line rather than a dashed one. A solid line tells us "points on the boundary are part of the solution set". The inclusion is because of the "or equal to" portion.
Change the equal sign to a less than or equal to sign to get the final answer of [tex]y \le -\frac{1}{3}x+1[/tex] which is choice B.
