Question

Find the slope of the graph of the linear function \(f\). $$ f(-1)=2, f(3)=2 $$

Short answer

The slope of the graph of the given linear function is 0.

Step-by-step solution

Identify Known Values

The function f's values are given for two specific x coordinates: f(-1) = 2 and f(3) = 2. Here, -1 and 3 are the x-coordinates \(x_1\) and \(x_2\), respectively, and 2 and 2 are the corresponding y-coordinates \(y_1\) and \(y_2\), respectively.

Substitute Values into Slope Equation

Using the slope equation \(m = (y_2 - y_1)/(x_2 - x_1)\), you insert the known x and y values. This gives \(m = (2 - 2)/(3 - -1)\).

Simplify the Equation to Find the Slope

Simplifying the denominator, you get \(m = (2 - 2)/(3 + 1)\). Further simplifying both the numerator and the denominator, the equation transforms into \(m = (0)/(4)\). Obtaining the final result, \(m = 0\). Hence, the slope is 0.