A decreasing linear function is a linear function with a negative slope, so as x increases, f(x) decreases. In College Algebra, it shows up as a straight line slanting downward from left to right.
A decreasing linear function in College Algebra is a linear function whose output gets smaller as the input gets larger. The standard form is f(x) = mx + b, and the defining feature is that the slope m is negative.
That negative slope tells you the rate of change. For every 1 unit you move right on the graph, the line goes down by the same fixed amount. So if a line has slope -3, each step to the right drops the output by 3. The change is constant, which is what makes the function linear in the first place.
You can spot a decreasing linear function by looking at its graph. The line slopes downward from left to right. That visual pattern matches the algebra: a negative slope means the y-values shrink as x-values grow. The y-intercept b is just where the line crosses the y-axis, so it shifts the line up or down but does not decide whether the function increases or decreases.
A quick example is f(x) = -2x + 5. If x = 0, the output is 5. If x = 1, the output is 3. If x = 2, the output is 1. Each time x increases by 1, f(x) drops by 2, which is exactly what decreasing means here.
This idea also connects to sequence and model questions in College Algebra. A steady decrease over equal x-values can represent something like depreciation, cooling, or a shrinking balance. The main thing to watch for is confusing the y-intercept with the slope. The intercept tells you where the line starts on the graph, but the slope tells you whether the function is increasing, decreasing, or constant.
Decreasing linear functions show up any time College Algebra asks you to read a trend, write an equation from a graph, or interpret a real-world pattern with steady decline. Once you know the slope is negative, you can predict what happens without calculating every point.
This term also connects several core skills in the course. You may need to identify the slope from a table, graph a line from an equation, or decide whether a story describes a rise, fall, or no change. That means you are not just memorizing a graph shape, you are translating between words, tables, equations, and visuals.
It matters in word problems too. A depreciation problem, for example, often starts with an item value that drops by the same amount each year. If the value goes down by a fixed dollar amount, the model is linear and decreasing. If the drop gets smaller each time, then the situation is no longer linear.
This term also sets up later function ideas. When you compare a decreasing linear function to a constant function or a nonlinear function, you get better at recognizing which kinds of change are steady and which are not. That skill shows up everywhere from graph interpretation to short-answer explanations on homework and quizzes.
Keep studying College Algebra Unit 3
Visual cheatsheet
view gallerySlope
Slope is the number that tells you the direction and steepness of a line. For a decreasing linear function, slope is negative, so the line goes down as you move right. If you can identify slope from two points or from an equation, you can tell right away whether the function is decreasing.
Linear Equation
A decreasing linear function is often written as a linear equation in slope-intercept form, f(x) = mx + b. The equation tells you both the starting value and the rate of change. In this setting, the negative value of m is what makes the function decrease.
Y-Intercept
The y-intercept tells you where the graph crosses the y-axis, which is the value when x = 0. It can change the vertical position of the line, but it does not affect whether the line is increasing or decreasing. That part comes from the slope.
Arithmetic Mean
Arithmetic mean is the average of a set of numbers, and it can show up when you summarize data that seems to follow a linear trend. If a data set has a steady downward pattern, the average change between terms may match the negative slope of a decreasing linear model.
A quiz question might give you an equation, table, or graph and ask whether the function is increasing, decreasing, or constant. Your move is to check the slope or compare outputs as x values rise. If the slope is negative, the function is decreasing, and if the graph slants downward from left to right, that is the visual clue.
You may also be asked to write an equation for a situation like depreciation. In that case, identify the starting value as the y-intercept and the fixed drop as the negative slope. On graphing problems, be ready to mark the intercept first, then use the slope to plot the rest of the line.
A decreasing linear function and a constant function can both be drawn as straight lines, but they behave differently. A constant function stays flat because its slope is 0, while a decreasing linear function has a negative slope and drops as x increases. If you see a line that never goes up or down, it is constant, not decreasing.
A decreasing linear function is a linear function with a negative slope.
As x increases, the output goes down by the same amount each time.
The graph is a straight line that slants downward from left to right.
The y-intercept tells you where the line crosses the y-axis, but the slope tells you whether it decreases.
Steady decline problems, like depreciation, are common places to model this type of function in College Algebra.
It is a linear function with a negative slope, which means the output gets smaller as the input gets larger. Its graph is a straight line that moves downward from left to right. The change is constant, so every step right changes the output by the same amount.
Check the slope. If the slope is negative, the function is decreasing. You can also look at the graph, where a decreasing line falls as you move from left to right. A table with outputs that get smaller as inputs increase shows the same pattern.
No. The y-intercept only tells you where the graph crosses the y-axis. It can move the line up or down, but it does not change the direction of the line. The slope is what decides whether the function increases, decreases, or stays constant.
It looks like a straight line slanting downward from left to right. The left side is higher and the right side is lower. If the line is flat, it is constant, and if it rises from left to right, it is increasing instead.