Question

How do I find the instantaneous slope at a point. I just need a brief explanation.

Answer 1

Take the derivative at that point.

Answer 2

If the line is a straight line then the slope is constant at all points on the line.

If you have an equation for the line y=f(x) then take the derivative (dy/dx or f'(x) )

Take the value of x at which you want the slope and put that value in the equation for f'(x). Evaluate that equation and that is the value of the slope at that point

Answer 3

for example

y=f(x)=x^2
dy/dx = f'(x) = 2x

at the point x=2.5 f'(2.5)= 2(2.5)= 5