# How do you write an equation of a line passing through (8, 2), perpendicular to 4x - y = 12?

The equation of line is $y = - \frac{1}{4} x + 4$
Comparing with the equation of line in slope-intercept form $y = m x + c$
we get the slope of the line $4 x - y = 12 \mathmr{and} y = 4 x - 12$ as ${m}_{1} = 4$
The slope of the perpendicular line is ${m}_{2} = - \frac{1}{m} _ 1 = - \frac{1}{4} \therefore$
The equation of line passing through$\left(8 , 2\right)$is $y - {y}_{1} = {m}_{2} \left(x - {x}_{1}\right) \mathmr{and} y - 2 = - \frac{1}{4} \left(x - 8\right) \mathmr{and} y = - \frac{1}{4} x + 4$[Ans]