Question

What is the slope if the line is differeniable.

Answer 1

Step-by-step explanation:

you mean "differentiable" ?

well, remember, a line equation is

y = ax + b

a is the slope

it is always, ALWAYS the factor of x.

now we differentiate the line equation per dx/dy

y' = a

and that is that.

the first derivative of an equation of first degree (that means the highest exponent of the variable is 1), which is a line equation, is a constant : the factor of x.

and since the factor of x is the slope, that means that the constant result of the first derivative of the line equation is the slope.