Slope from 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 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 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

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 (change in y) and run (change in x), and use the slope formula: m = rise/run.

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, calculate the change in y (Δy) and the change in x (Δx) between two points, then use the formula: slope = Δy/Δx.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the points (2, 3) and (5, 9)?

Back

The slope is (9 - 3) / (5 - 2) = 6 / 3 = 2.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the points (1, 4) and (3, 2)?

Back

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

Tags

CCSS.8.EE.B.5