Linear Functions

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 the y-value with respect to the x-value. It indicates how steep the line is.

Front

How do you calculate 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 y-intercept in a linear equation?

Back

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

Front

If a line has a slope of 4, what does this mean?

Back

A slope of 4 means that for every 1 unit increase in x, the value of y increases by 4 units.

Front

What is the slope of a line that goes down from left to right?

Back

The slope of a line that goes down from left to right is negative.

Front

What is the equation of a line with a slope of 1/2 and a y-intercept of 3?

Back

The equation of the line is y = (1/2)x + 3.

Front

How can you determine which of two lines has a greater rate of change?

Back

The line with the greater slope has a greater rate of change.

Front

What does it mean if two lines are parallel?

Back

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

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.