Question

1. what is the slope of the secant line that passes through the points (a, f(a)) and (b, f(b)) on the graph of f?

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

For the points \((a, f(a))\) and \((b, f(b))\), we have \( x_1 = a \), \( y_1 = f(a) \), \( x_2 = b \), and \( y_2 = f(b) \).

Step3: Substitute into the slope formula

Substituting these values into the slope formula, we get \( m=\frac{f(b)-f(a)}{b - a} \).

Answer:

The slope of the secant line is \(\frac{f(b)-f(a)}{b - a}\)