Question

Write an equation in slope-intercept form for a line perpendicular to the graph of the equation that passes through the x-intercept of that line

y=-1/2x-4
The answer to this is y=2x+16 and I don't know how the book got there, please explain.

Answer 1

Okay.
We know that a perpendicular slope to an original function is the normal line of the original function's slope. Opposite reciprocal.
If the slope is 2x, the perpendicular line's slope is -1/2x.
If the slope is 2/5 x, the perpendicular line's slope is -5/2x.
If the slope, in this case, is -1/2x, then the perpendicular line's slope is 2/1x.

So, if the equation is y=-1/2x -4, then the perpendicular line will be y=(2/1x )+some number.
Mathematically, what did it take to get from -1/2 to 2/1? Multiplied by negative four (other than the opposite reciprocal trick.)
So your constant will be multiplied by -4.
-4 times -4 = 16.
So your equation is y=(2/1)x + 16.

Answer 2

Thank you! @hink