Questions: Use the equation Q=(f(x)-f(a))/(x-a) to find the slope of the secant line given f(x)=4x+9; x₁=3, x₂=6.

Solution Steps

To find the slope of the secant line for the function \( f(x) = 4x + 9 \) between the points \( x_1 = 3 \) and \( x_2 = 6 \), we will use the formula for the slope of the secant line:

\[ Q = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \]

1. Calculate \( f(x_1) \) and \( f(x_2) \) using the given function.
2. Substitute these values into the secant slope formula to find \( Q \).

The function given is

\[ f(x) = 4x + 9 \]

We need to evaluate the function at the points \( x_1 = 3 \) and \( x_2 = 6 \):

\[ f(3) = 4(3) + 9 = 12 + 9 = 21 \]

\[ f(6) = 4(6) + 9 = 24 + 9 = 33 \]

Using the secant slope formula

\[ Q = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \]

we substitute the values we calculated:

\[ Q = \frac{33 - 21}{6 - 3} = \frac{12}{3} = 4 \]

Final Answer