Finding 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, 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 from two points (x1, y1) and (x2, y2)?

Back

Slope (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, meaning the line rises from left to right.

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, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

If a line rises 4 units for every 5 units it runs, what is the slope?

Back

The slope is 4/5.

Front

If a line falls 3 units for every 4 units it runs, what is the slope?

Back

The slope is -3/4.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope, representing how much the output (y) changes for a change in the input (x).

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope by selecting two points on the line, measuring the vertical and horizontal distances between them, and calculating the rise over run.