From Proportions to Linear Relationships Summary

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you represent a proportional relationship mathematically?

Back

A proportional relationship can be represented by the equation y = kx, where k is the constant of proportionality.

Front

What is the constant of proportionality in a relationship?

Back

The constant of proportionality is the ratio of the dependent variable to the independent variable in a proportional relationship.

Front

If 2 out of every 5 balloons are red, how can this be expressed as an equation?

Back

The equation is y = (2/5)x, where y is the number of red balloons and x is the total number of balloons.

Front

What does a rate of change represent in a linear relationship?

Back

The rate of change represents how much the dependent variable changes for a unit change in the independent variable.

Front

How can you determine if a relationship is proportional from a graph?

Back

A relationship is proportional if the graph is a straight line that passes through the origin.

Front

What is the formula to find the rate of change between two points (x1, y1) and (x2, y2)?

Back

The rate of change is calculated as (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the rate of change between the variables.

Front

How do you identify a greater rate of change in equations?

Back

A greater rate of change can be identified by comparing the slopes of the equations; the one with the larger absolute value of the slope has a greater rate of change.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal.