Slope 11.24

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 is slope calculated?

Back

Slope is calculated using the formula: Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 (rise) regardless of the horizontal change (run).

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 (run) is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

In the slope formula, what do 'rise' and 'run' refer to?

Back

'Rise' refers to the vertical change between two points, while 'run' refers to the horizontal change between those same two points.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of -1/3, what does this tell you about its steepness?

Back

A slope of -1/3 indicates that for every 3 units moved horizontally to the right, the line moves down 1 unit, resulting in a gentle downward slope.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope of the line represented by the equation y = 2x + 1 is 2, indicating that for every 1 unit increase in x, y increases by 2 units.

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 various contexts, such as speed, cost per item, or growth rates, making it essential for interpreting data.

Tags

CCSS.8.EE.B.5