I need it step by step please

1/2x-3

Step-by-step explanation:

First, make the equation 2y+4x=12 into a linear equation(y=mx+b)

2y=-4x+12

y=-2x+6

From this, you know the slope is -2.

The perpendicular of any slope is going to be the negative inverse.

negative inverse: a/b-->-b/a

so basically flip it and make it negative(make it positive if the original is negative).

So, for -2 it would be 1/2

Now right the equation for the perpendicular line.

y=1/2x+b

b is the y intercept, and since you want to make the line go through (8,1) you have to change the 6 in the original equation.

To do this replace x and y with 8 and 1

1=1/2(8)+b

1=4+b

b=-3

So you plug that into the equation

y=1/2x-3

2y+4x=12

Move 4x to the other side as a negative number

2y=-4x+12

Divide all terms by 2

y=-2x+6

Now, in order for two lines to be perpendicular, their gradients have to multiply obeyed to get -1 (let a be the gradient of the given line and let b be the gradient of the line we're trying to find)

So, we do -2*b=-1

so, b is equal to 1/2

Now, we are given a coordinate so we substitute it in y-y1=m(x-x1)

y-1=1/2(x-8)

Expand brackets

y-1= 1/2x-4

Take -1 to the other side as a positive number

y=1/2x-3

So, the equation of the line is y=1/2x-3

srry i dont understand the question