Question

What is the slope of a line perpendicular to the line with equation y = 4x + 5?

Answer 1

The slope of the given line can be obtained by differentiating the given equation w.r.t x.
Then you end up \[dy/dx=4\]
There is a theory in coordinate geomatry that if to lines are perpendicular and the their gradients are m1 and m2 respectively then they satisfy the equation, \[m _{1}*m _{2}=-1\]
So your final answer would be -1/4

Answer 2

y=4x+5
m=4...slope of the given line which parallel
m_n=slope of normal line(perpendicular line) m=-1/4