Question 508812
y = -3x
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The slope is -3.
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The slope of a perpendicular line is the inverse reciprocal:  1/3.
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So, the equation is
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y = 1/3x + b
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To find 'b' we can use the point we want the line to go through.
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(-1/2,3/2) = (x, y)
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3/2 = 1/3(-1/2) + b
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3/2 = -1/6 + b
b = 9/6 + 1/6
b = 10/6
b = 5/3
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y = 1/3x + 5/3
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The following graph shows the y = -3x in red and y = 1/3x+5/3 in green
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{{{graph(500,500,-6,6,-6,6,-3*x,1/3*x+5/3)}}}