Graph Linear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be written 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 y-value with respect to the x-value. It shows how steep the line is.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the slope from two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is y = b, where b is the y-value for all points on the line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is x = a, where a is the x-value for all points on the line.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and 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. This means they intersect at a right angle.

Front

How can you determine if a point lies on a line?

Back

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

Front

What is the average rate of change?

Back

The average rate of change between two points on a line is the change in y divided by the change in x, often interpreted as the slope.