Write an equation in pointslope for of the line through the

Write an equation in point-slope for of the line through the point (-3, 2) perpendicular to the line with equation 2x + 3y = 5.

Solution

Given a point is (-3,2) and a line is 2x + 3y = 5.

Required line is perpendicular to 2x + 3y = 5.

Means multiplication of required line slope and given equation slope is -1.

Let required line slope is m.

Given line slope is -2/3.

(m)(-2/3) = -1

m = (-1)(-3/2)

m = 3/2

Point-slope form of a line is y -y1= m(x-x1)

Substitute slope(m) =3/2 and a point (x1, y1) = (-3,2)

y -y1= m(x-x1)

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

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

equired line equation is y - 2 = (3/2)(x+3)