Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the equation of a line with a slope of 3 and a y-intercept of -2?

Back

The equation of the line is y = 3x - 2.

Front

What does it mean if a line has a positive slope?

Back

A positive slope means that as the x-value increases, the y-value also increases, indicating a direct relationship.

Front

What does it mean if a line has a negative slope?

Back

A negative slope means that as the x-value increases, the y-value decreases, indicating an inverse relationship.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

How can you determine if one linear function has a greater rate of change than another?

Back

You can compare the slopes of the two functions; the function with the larger absolute value of the slope has a greater rate of change.