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 from a table of values?

Back

To calculate the slope from a table of values, select two points (x1, y1) and (x2, y2) from the table, and use the formula: slope (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 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 in the slope formula.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the points (1, 2) and (3, 8)?

Back

The slope is calculated as (8 - 2) / (3 - 1) = 6 / 2 = 3.

Tags

CCSS.8.EE.B.5

Front

How can you interpret a slope of -3 in a real-world context?

Back

A slope of -3 indicates that for every 1 unit increase in the x-variable, the y-variable decreases by 3 units, which could represent a decrease in a quantity over time or distance.

Tags

CCSS.8.EE.B.5

Front

What is the significance of a slope of 1/2?

Back

A slope of 1/2 indicates that for every 2 units of horizontal change (run), there is a 1 unit increase in vertical change (rise), suggesting a gradual incline.

Tags

CCSS.8.EE.B.5