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 from 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 slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate about the relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about the relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

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

Back

A slope of 2 means that for every 1 unit you move horizontally (run), the line rises 2 units vertically (rise).

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 vertical change (rise) and the horizontal change (run) between them, and use the slope formula: m = rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line represented by the equation y = 3x + 1 is 3.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in real-world contexts, such as speed, cost per item, or growth rates.

Tags

CCSS.8.EE.B.5