Slope from a Graph

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).

Front

How do you calculate the slope of a line using 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?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (run = 0), making the slope calculation impossible.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no vertical change (rise = 0) as the x-value changes.

Front

If a line rises 4 units and runs 2 units, what is the slope?

Back

Front

If a line falls 3 units and runs 6 units, what is the slope?

Back

Front

What is the slope of a line that passes through the points (1, 2) and (3, 6)?

Back

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise (vertical change) and run (horizontal change), and calculate the slope using the rise/run formula.