# A line perpendicular to y = 1/4x + 3 passes through the point (0,6). Which other point lies on the line?

May 25, 2018

color(brown)(4x + y = 6

#### Explanation:

$y = \left(\frac{1}{4}\right) x + 3$

It’s in slope-intercept form $y = m x + c$

Slope $m = \left(\frac{1}{4}\right)$

Slope of perpendicular line $= - \left(\frac{1}{m}\right) = - 4$

Point-slope equation form is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Equation of the perpendicular line passing through point (0,6) is

$y - {y}_{1} = - \left(\frac{1}{m}\right) \left(x - {x}_{1}\right)$

$y - 6 = - 4 \left(x - 0\right)$

color(brown)(4x + y = 6