Write the equation of a line that is perpendicular to the given line and that passes through the given point. y + 2 = 1/3(x-5) ; (-4, 3)

The equation would be y = -3x - 9

Step-by-step explanation:

Since we have the slope of 1/3, we know the slope of a perpendicular line would be -3. This is because perpendicular lines have opposite and reciprocal slopes. We can then use this and the point to solve in point-slope form.

y - y1 = m(x - x1)

y - 3 = -3(x + 4)

y - 3 = -3x - 12

y = -3x - 9

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2