Slope (Multiple Representations)

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 to the horizontal change 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Tags

CCSS.8.EE.B.5

Front

If the slope of a line is positive, what does that indicate about the line's direction?

Back

A positive slope indicates that the line rises as it moves from left to right.

Tags

CCSS.8.EE.B.5

Front

If the slope of a line is negative, what does that indicate about the line's direction?

Back

A negative slope indicates that the line falls as it moves from left to right.

Tags

CCSS.8.EE.B.5

Front

What does a slope of 1/2 represent in terms of rise over run?

Back

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

Tags

CCSS.8.EE.B.5

Front

How can slope be represented in a linear equation?

Back

In a linear equation of the form y = mx + b, 'm' represents the slope of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form 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

How does the slope relate to the rate of change in a real-world context?

Back

The slope represents the rate of change of one quantity with respect to another, such as speed (distance over time) or cost (price over quantity).

Tags

CCSS.8.EE.B.5