Decreasing linear function

Definition

A decreasing linear function is a linear function where the value of the function decreases as the input increases. It has a negative slope.

5 Must Know Facts For Your Next Test

1. A decreasing linear function can be represented by $f(x) = mx + b$ where $m < 0$.
2. The graph of a decreasing linear function is a straight line that slopes downward from left to right.
3. The y-intercept ($b$) is where the line crosses the y-axis, but it does not affect whether the function is increasing or decreasing.
4. The rate of change in a decreasing linear function is constant and equal to the slope ($m$).
5. In real-world scenarios, decreasing linear functions can model situations like depreciation over time.

Review Questions

Related terms

Slope:

The measure of steepness or incline of a line, represented by $m$ in the equation $y = mx + b$. In a decreasing linear function, $m < 0$.

Linear Equation:

An algebraic equation in which each term is either a constant or the product of a constant and a single variable. It forms a straight line when graphed.

Y-Intercept: The point where the graph of a function crosses the y-axis, represented by $b$ in the equation $y = mx + b$. This value does not determine whether the function is increasing or decreasing.