Rate of Change and Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the rise (vertical change) to the run (horizontal change) between two points on the line.

Front

How do you calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

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 vertical change as you move along the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as you move from left to right, the line goes down.

Front

What is the significance of a slope of -2?

Back

A slope of -2 means that for every 1 unit you move to the right (run), the line goes down 2 units (rise).

Front

What is a proportional relationship in the context of a graph?

Back

A proportional relationship is represented by a straight line that passes through the origin (0,0), indicating a constant ratio between the two variables.

Front

How can you determine if a graph represents a proportional relationship?

Back

You can determine if a graph represents a proportional relationship by checking if the line passes through the origin and is straight.

Front

What is the formula for calculating the rate of change?

Back

The rate of change is calculated as the change in the dependent variable divided by the change in the independent variable, often expressed as (change in y) / (change in x).

Front

What does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the vertical change (rise) divided by the horizontal change (run) when calculating the slope of a line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (horizontal change) is 0, leading to division by zero.