Slope and Rate of Change Practice

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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 an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined rate of change.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

If a line passes through the points (2, 4) and (6, 12), what is the slope?

Back

The slope is 2, calculated as (12 - 4) / (6 - 2).

Front

What is the rate of change in the context of a linear function?

Back

The rate of change refers to how much the output (y) changes for a given change in the input (x), which is represented by the slope of the line.

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope is 3/4, calculated as rise/run.

Front

What is the slope of a line that falls 5 units for every 2 units it runs?

Back

The slope is -5/2, indicating a negative slope.

Front

How can you determine if a line is increasing or decreasing based on its slope?

Back

If the slope is positive, the line is increasing; if the slope is negative, the line is decreasing.

Front

What is the slope of a line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.