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 (rise) to the horizontal change (run) between two points on the line.

Tags

CCSS.8.EE.B.5

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).

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-values increase, the y-values also increase, 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-values increase, the y-values decrease, meaning the line falls from left to right.

Tags

CCSS.8.EE.B.5

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Tags

CCSS.8.EE.B.5

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-values do not change while the y-values do, leading to division by zero in the slope formula.

Tags

CCSS.8.EE.B.5

Front

If the slope of a line is 1/2, what does this imply about the rise and run?

Back

A slope of 1/2 implies that for every 2 units of horizontal change (run), there is a 1 unit vertical change (rise).

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 apply the slope formula: m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that goes through the points (2, 3) and (4, 5)?

Back

The slope is (5 - 3) / (4 - 2) = 2 / 2 = 1.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.

Tags

CCSS.8.EE.B.5