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 y = 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 represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you find 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 equation of a line with a slope of 1 and a y-intercept of 0?

Back

The equation is y = 1x + 0, or simply y = x.

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning that the y-value remains constant regardless of the x-value.

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.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant for equal intervals of x.

Front

What is the significance of the point (0, b) in a linear function?

Back

The point (0, b) represents the y-intercept, where the line crosses the y-axis.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.