Slope and Rate of Change

Front

What is the definition of slope?

Back

The slope is a measure of the steepness of a line, calculated 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) is 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-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.

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 there is no horizontal change.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of 4/5, what does this mean in terms of rise and run?

Back

A slope of 4/5 means that for every 5 units moved horizontally (run), the line rises 4 units (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 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 slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the rate of change in a real-world context?

Back

The rate of change describes how one quantity changes in relation to another, often represented by the slope in a graph.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6