Analyzing 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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

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 as (0, b) in the equation y = mx + b.

Front

True or False: A line with a positive slope rises from left to right.

Back

True

Front

True or False: A line with a negative slope falls from left to right.

Back

True

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

True or False: The graph of a direct variation has a y-intercept of zero.

Back

True

Front

How can you determine if a point lies on a line represented by a linear equation?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.