Find the equation of the line that is perpendicular to y=-4x +8 and passes through the point (-12,4)

y = x/4 + 7

Step-by-step explanation:

Step1: find the slope

y = -4x + 8

Slope is the coefficient of x

ie m = -4

Since the line is perpendicular,

Note that if two lines are perpendicular to the other, the lines are negative reciprocal of each other

m = 1/4

Step 2: using a point slope form equation

y - y1 = m( x - x1)

( -12 , 4)

x1 = -12

y1 = 4

y - 4 = 1/4( x -(-12)

y - 4 = 1/4( x + 12)

Step 2 : using the slope intercept form equation

y = mx + c

Open the bracket

y - 4 = ( x + 12)/4

y = ( x + 12)/ 4 + 4

LCM = 4

y = ( x + 12) + 16 / 4

y = x + 12 + 16 / 4

y = x + 28 / 4

We need to separate it to get the slope and the intercept

y = x/4 + 28/4

y = x/ 4 + 7

The equation of the line is

y = x/4 + 7

associative property of multiplication

linear pair postulates