Describing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

How do you find the y-intercept of a linear function?

Back

The y-intercept of a linear function is found by setting x = 0 in the function's equation and solving for y.

Front

What is the x-intercept of a linear function?

Back

The x-intercept of a linear function is the point where the graph crosses the x-axis, found by setting y = 0 in the function's equation and solving for x.

Front

How do you determine the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, as the output can take any value depending on the slope and y-intercept.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through these points.

Front

What does it mean for a linear function to be increasing or decreasing?

Back

A linear function is increasing if the slope is positive (m > 0) and decreasing if the slope is negative (m < 0).