Slope - Proportional Relationships

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a graph?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a graph?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

Front

How can you interpret a slope of 2 in a real-world context?

Back

A slope of 2 means that for every 1 unit increase in the x-variable, the y-variable increases by 2 units.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What does it mean if a graph has an undefined slope?

Back

An undefined slope occurs in a vertical line where the x-value does not change, leading to division by zero in the slope formula.

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine their coordinates, and apply the slope formula.

Front

What is the relationship between slope and proportional relationships?

Back

In proportional relationships, the slope represents the constant ratio between the two quantities, indicating a direct variation.