Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the rise (change in y) to the run (change in x). It is often represented by the letter m in the equation of a line.

Front

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

Back

To find the y-intercept of a linear equation in the form Ax + By = C, set x = 0 and solve for y.

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis. It can be found by setting y = 0 and solving for x.

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

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What does the term 'rise over run' refer to?

Back

'Rise over run' refers to the calculation of the slope of a line, representing the vertical change (rise) divided by the horizontal change (run) between two points on the line.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the value of y when x = 0. It indicates where the line crosses the y-axis and is represented by the point (0, b) in the equation y = mx + b.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line in the Cartesian plane, where m is the slope and b is the y-intercept.