the equation of a line is of the form y = mx + b, where m is the slope (given by the derivative) and b is the y-intercept.

if we know the slope and a point the line passes through, we can find the equation of the line by using the point-slope form:

that is, solve for .

where is the slope, and is a point the line passes through

Note: for the equation of the NORMAL, we find the line that is PERPENDICULAR to the tangent line that touches the graph at the same point the tangent line does

we find the horizontal tangent line by finding the point where the slope is zero, and using the same point-slope form

any questions?