The solid line has the boundary equation y = -x+4 This line goes through (0,4) and (4,0). Using the slope formula, we find that m = -1. Plugging m = -1 and (x,y) = (0,4) into y = mx+b leads to y = -x+4
The shading is below the solid line so we change the equal sign to a "less than or equal to" sign, which leads us to y <= -x+4
That takes care of the first inequality. We must use "or equal to" as part of the inequality to ensure the boundary is solid
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The second inequality is y > (1/3)x as the boundary line is y = (1/3)x. This line goes through (0,0) and (3,1). The slope is 1/3 and y intercept is 0
The boundary is a dashed line. This means we don't have "or equal to" as part of the inequality
