8-(4-1) Rate of Change/Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 does a positive slope indicate about a line?

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 line?

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 no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the change in x is zero, indicating that the line does not rise or fall.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much the output (y) changes for a unit change in the input (x).

Front

How can you identify the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is zero.