Question

Find the equation perpendicular to the line y=−3x+5 that passes through point (2, 6).

Answer 1

For a line to be perpendicular, the product of its slope and the given slope must be equal to -1
so..
$\frac{ - 1}{ - 3} = \frac{1}{3}$

now we need to find our y-intercept
we use the given coordinate and our new slope find this
$y - intercept = 5 \frac{1}{3} = \frac{16}{3}$

now to put these together into our final equation
$y = \frac{1}{3} x + \frac{16}{3}$

Answer 2

Perpendicular lines have slopes whose product is -1.

If the original line has slope 3, the line that is perpendicular has slope -(1/3) Now use the point slope form of the line.

y - y1 = m(x - x1)

If (x1,y1) = (2,2) - your point, then:

y - 2 = (-1/3)(x - 2)

you can convert this into slope-intercept form.

y - 2 = (-1/3)x + (2/3)

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

Both equations represent the same line.