Slope and Rate of Change

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, 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 on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, showing a direct relationship.

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, showing an inverse relationship.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

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 given change in the input (x).

Front

How can you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in real-world applications?

Back

In real-world applications, the slope can represent rates such as speed, cost per item, or any other ratio of change between two quantities.

Front

What does 'rate of change' refer to in a mathematical context?

Back

Rate of change refers to how one quantity changes in relation to another quantity, often expressed as a ratio or slope.