Question

Find the slope of the graph of the linear function \(f\). $$f(0)=5, f(5)=0$$

Short answer

The slope of the linear function f(x) is -1

Step-by-step solution

Identify the given coordinates

Identify the coordinates for two points on the line from the given function. The first point is at x = 0, which is (0, 5) because f(0) = 5. The second point is at x = 5, which is (5, 0) because f(5) = 0.

Use the slope formula

Using the slope formula, calculate the slope. The slope formula is: \(slope = \frac{change in y}{change in x} = \frac{y2 - y1}{x2 - x1}\). With the given points (0, 5) and (5, 0), apply this into the formula as follows: \(slope = \frac{0-5}{5-0}\).

Simplify the equation

Simplifying the equation gives: \(slope = \frac{-5}{5} = -1\)