Write the equation of a line that is perpendicular to y =
x + 6 and that passes through the point (2,-6).

y = -x - 4

Step-by-step explanation:

Step 1: find slope

y = x + 6

Slope m = 1

y = mx + c

The coefficient of x is the slope

Step 2 : substitute m into the point slope form equation

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

m = - 1

y - y1 = m( x - x1)

y - y1 = -1(x - x1)

Step 3: sub the point

( 2 , -6)

x1 = 2

y1 = -6

y - (-6) = -1( x - 2)

y + 6 = -1(x - 2)

Open the bracket

y + 6 = -x + 2

y = -x + 2 - 6

y = -x - 4

The equation of a line is

y = -x - 4