Slope from a Graph

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, typically represented 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) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line on a graph?

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 positive slope indicate about the direction of a line?

Back

A positive slope indicates that the line rises from left to right.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that the line falls from left to right.

Front

What is the slope of a vertical line?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit you move horizontally (run), the line rises 2 units (rise).

Front

How can you determine the slope from a graph visually?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (vertical change) and run (horizontal change) between them, and then use the slope formula.

Front

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

Back

The slope can represent rates of change in various contexts, such as speed, cost per unit, or growth rates.