Need some help figuring this one out?

Question

Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6).

Answer 1

x + 2y = 8 can be rearranged as:
2y = 8 - x
y = 4 - x/2
y = -x/2 + 4

So the slope of the above equation is -1/2. Let's call it m1.

Let's denote m2 as the slope of the second line. The second line would be perpendicular to the first line if m1 x m2 = -1.

So: m1 x m2 = -1
-1/2 m2 = -1
m2 = 2

Plug in the point to the line equation:
y = m2 * x + b
-6 = 2(1) + b
-6 = 2 + b
b = -8

Therefore: y = 2x - 8 (this is the final answer.)

Answer 2

Write the equation in y= mx+ b format
y = -(1/2) x + 4
Any line perpendicular to this will have a slope of
-(1/m), which in this case is +TWO.
The specific line you want will satisfy x=1 and y=-6. So substitute in this pair of coords.
-6 = 2(1) +b , so b=-8.
You should be able to do this. It isn't so hard.