Linear Functions and Slope

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 (m) represent in a linear function?

Back

The slope (m) 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

What is the y-intercept (b) in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function at a specific point, substitute the x-value into the function and solve for f(x).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on its graph.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for finding the slope (m) between two points is m = (y2 - y1) / (x2 - x1).

Front

If f(x) = 2x + 1, what is f(1)?

Back

f(1) = 2(1) + 1 = 3.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases. This occurs when the slope (m) is positive.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases. This occurs when the slope (m) is negative.