Slope (from a table)

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 vertical change to the horizontal change between two points on the line.

Tags

CCSS.8.EE.B.5

Front

How is slope calculated from two points (x1, y1) and (x2, y2)?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

Front

If the slope of a line is 5, what does this mean in terms of rise over run?

Back

A slope of 5 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 5 units.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that rises 2 units for every 4 units it runs?

Back

The slope is 1/2, calculated as rise/run = 2/4.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope can represent rates of change, such as speed, growth, or efficiency, in various real-world contexts.

Tags

CCSS.8.EE.B.5