Rate of change - graphs

Front

What is the definition of slope in the context of a graph?

Back

The slope of a line is a measure of its steepness, 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 of a line given 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 it would involve division by zero (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 interpret a slope of -1 in a real-world context?

Back

A slope of -1 indicates that for every unit increase in x, there is a corresponding unit decrease in y, suggesting a direct inverse relationship.

Front

What does a slope of -6 represent in terms of rate of change?

Back

A slope of -6 means that for every 1 unit increase in x, the value of y decreases by 6 units.

Front

What is the significance of the slope in a graph representing speed over time?

Back

In a graph of speed over time, the slope represents acceleration; a positive slope indicates increasing speed, while a negative slope indicates decreasing speed.