# Thread: Write an expression for the slope of the secant line

1. ## Write an expression for the slope of the secant line

A curve has equation y = f(x)

(a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)).

(b) Write an expression for the slope of the tangent line at P.

2. Originally Posted by question111
A curve has equation y = f(x)

(a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)).

$\frac{f(x) - f(3)}{x - 3}$

(b) Write an expression for the slope of the tangent line at P.

$f'(3) = \lim_{x \to 3} \frac{f(x) - f(3)}{x - 3}$
ok?

3. for the first question, i believe its called the average rate of change formula.
$\frac{f(b) - f(a)}{ b-a}$

4. Thank you very much.