Linear Functions 2

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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

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 y = mx + b, set x = 0 and solve for y. The value of y when x = 0 is the y-intercept.

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. To find it, set y = 0 and solve 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 can you determine if a line is vertical?

Back

A line is vertical if it has an undefined slope, which occurs when all points on the line have the same x-coordinate.

Front

What does it mean if a line has a slope of zero?

Back

A line with a slope of zero is horizontal, meaning there is no change in y as x changes. The equation of such a line is y = b, where b is a constant.

Front

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

Back

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

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 is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they rise and run at the same rate and will never intersect.