Final answer:
To find the slope of the curve y = x^2 - 2x - 3 at the point P(2,-3), we can use the concept of secant slopes. To find an equation of the tangent line to the curve at P(2,-3), we will use the point-slope form of a linear equation.
Step-by-step explanation:
To find the slope of the curve y = x^2 - 2x - 3 at the point P(2,-3), we can use the concept of secant slopes. The secant slope is the slope of the line passing through two points on the curve. We will find the slope of the secant through point P by calculating the difference in y-coordinates and the difference in x-coordinates of two points on the curve close to P.
To find an equation of the tangent line to the curve at P(2,-3), we will use the point-slope form of a linear equation. The tangent line has the same slope as the curve at point P. We will substitute the coordinates of point P and the slope into the point-slope form to determine the equation of the tangent line.