Finding Slope from Tables and Graphs

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 in the slope formula.

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 use the slope formula: m = rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the steepness of a slope?

Back

The steepness of a slope indicates how quickly y changes with respect to x; a steeper slope means a greater change in y for a given change in x.

Tags

CCSS.8.EE.B.5

Front

How can you identify the steepest slope among multiple lines on a graph?

Back

To identify the steepest slope, compare the absolute values of the slopes of the lines; the line with the largest absolute value of slope is the steepest.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line represented by the equation y = 3x + 2 is 3, which is the coefficient of x.

Tags

CCSS.8.EE.B.5