Finding Slopes through Graphs and Tables

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 using rise over run?

Back

To calculate the slope using rise over run, you take the difference in the y-coordinates (rise) and divide it by the difference in the x-coordinates (run) between two points on the line: 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-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 (rise) regardless of the horizontal change (run).

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 run is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (vertical change) and run (horizontal change) between them, and then calculate the slope using the formula: Slope = rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line represented by the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, indicating how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the significance of a slope of 1?

Back

A slope of 1 indicates that for every unit increase in x, there is an equal unit increase in y, resulting in a 45-degree angle line.

Tags

CCSS.8.EE.B.5