Find the equation of a line perpedicular to the line
y=-3x+2 and passes through the point (6,8)

y = 1/3x + 6

Step-by-step explanation:

Using the equation of line

y = mx + C

y - y_1 = m( x - x_1)

First find the slope of the line

y = -3x + 2

Note, if two lines are perpendicular, their slope will be negative reciprocal

Ie m = 1/3

Using the equation now

y - y_1 = m(x - x_1)

With point (6 , 8)

x_1 = 6

y_1 = 8

y - 8 = 1/3(x - 6)

y -8 = (x - 6)/3

y = (x - 6)/ 3 + 8

Lcm is 3

y = x - 6 + 24/3

y = x + 18/ 3

We can separate

y = x / 3 + 18/ 3

y = x /3 + 6

y = 1/3x + 6

The equation of the line is

y = 1/3x + 6