3.4-3.5 Slope and Unit Rate

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline 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

Slope (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 unit rate?

Back

The unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per 1'.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

If a car travels 300 miles using 10 gallons of gas, what is the unit rate of miles per gallon?

Back

Unit rate = 300 miles / 10 gallons = 30 miles per gallon.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What does an undefined slope represent?

Back

An undefined slope represents a vertical line where the change in x is zero, making the slope calculation impossible.

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

How can you interpret the slope in a real-world context?

Back

In a real-world context, the slope can represent rates of change, such as speed (distance over time) or cost per item.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the slope in a graph representing distance vs. time?

Back

In a distance vs. time graph, the slope represents speed; a steeper slope indicates a faster speed.

Tags

CCSS.8.EE.B.5