To determine if a function is linear, we can analyze its equation. A linear function can be expressed in the form y = mx + b, where m represents the slope and b is the y-intercept. A key characteristic of linear functions is that they graph as straight lines.
In contrast, nonlinear functions do not adhere to this format. They might involve exponents (other than one), trigonometric functions, or other operations that create curves or bends in the graph.
Steps to Determine:
- Examine the equation of the function.
- If it’s in the form of y = mx + b, it’s linear.
- If it features variables raised to powers greater than one, or if it includes products or more complex operations, it’s likely nonlinear.
Finding the Slope:
If you determine that the function is linear, the slope (m) can be found directly from the equation. For instance, in the equation y = 2x + 3, the slope is 2. This means that for every unit increase in x, the value of y increases by 2.
In summary, carefully analyze the equation to classify the function as linear or nonlinear, and if it’s linear, directly extract the slope from its equation.