Slopes of Linear Functions

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value does not change, leading to a division by zero in the slope formula.

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

If a linear function has a slope of -1/4, what does this tell you about the function's behavior?

Back

A slope of -1/4 indicates that for every 4 units the line moves to the right (positive x-direction), it moves down 1 unit (negative y-direction).

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a perfectly horizontal line is zero.

Front

If a linear function has a slope of 4, what does this mean in terms of rate of change?

Back

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