Question

Write an equation of the line that passes through the given point and is

perpendicular to the given line.
y = 2/3 x + 1 (3,-2)

Answer 1

since the equation of the line passing through the given point is perpendicular to the given line(m2= -1/m1)

using the formula y=mx+c

y=2/3x +1

m1=2/3

m2= -1/2/3

m2= -3/2

the slope of the second line is -3/2 and it passes through the point(3,-2)

using the formula y-y1 = m(x-x1)

y-(-2)= -3/2(x-3)

y+2= -3/2(x-3)

multiply both sides by 2

2(y+2) = -3(x-3)

2y+4 = -3x+9

2y = -3x+5

y= -3/2x + 5/2