Slope and Rate of Change

Front

What is the definition of slope?

Back

Slope is a measure of the steepness 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 using two points (x1, y1) and (x2, y2)?

Back

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, indicating no vertical change as the x-value changes.

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 it represents a division by zero in the slope formula.

Tags

CCSS.8.EE.B.5

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 expressed as a slope in a graph.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a line has a slope of 4/3, what does this mean in terms of rise and run?

Back

A slope of 4/3 means that for every 3 units moved horizontally (run), the line rises 4 units (rise).

Tags

CCSS.8.EE.B.5

Front

How do you interpret a slope of -2 gallons per minute?

Back

A slope of -2 gallons per minute indicates that for every minute that passes, the quantity decreases by 2 gallons.

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 is 3, which means for every 1 unit increase in x, y increases by 3 units.

Tags

CCSS.8.EE.B.5