Secant/Tangent/Normal Lines

It is important for you to discern the difference between the aforementioned lines.

A secant line is a line that is drawn through two distinct points on a curve. To find the slope of the secant line you just find the change in y and divide by the change in x. Then all we need to do is plug it into point-slope form. y - yk =m (x - xk)

A tangent line is a line that is drawn through only one point on a curve. Right now, we find the slope of the tangent line by finding the limit as h goes to zero of the difference quotient (the change in y divided by the change in x) between our point x=a and a point immediately to the right, x=a+h. Once we do some algebra manipulation we will get a single number as the slope(m). Then all we need to do is plug it into point-slope form. y - yk =m (x - xk) This will be the equation for the tangent line through that single point (a, f(a))

A normal line is a line that is drawn through the same point on the curve as the tangent line was. It is perpendicular to the tangent, therefore its slope is -1/m. This means that only the slope needs to change from your tangent line equation when it is written in point-slope form.
y - yk =(-1/m)* (x - xk) This will be the equation for the normal line through that single point (a, f(a))

Example