Scaling & Proportions

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio to each other.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, often represented as y = kx.

Front

How can you determine if a graph represents a proportional relationship?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Front

What is the origin in a coordinate plane?

Back

The origin is the point where the x-axis and y-axis intersect, represented by the ordered pair (0,0).

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, a quantity, indicating how much larger or smaller a figure is compared to its original size.

Front

If a table shows values of x and y, how can you find the constant of proportionality?

Back

To find the constant of proportionality, divide the value of y by the corresponding value of x for any pair of values in the table.

Front

What is the relationship between proportionality and linear equations?

Back

Proportionality is represented by linear equations of the form y = kx, where k is the constant of proportionality.

Front

What does a straight line through the origin indicate in a graph?

Back

A straight line through the origin indicates a proportional relationship between the variables represented on the axes.

Front

How do you identify non-proportional relationships in a graph?

Back

Non-proportional relationships can be identified by graphs that do not pass through the origin or are not straight lines.

Front

What is the formula for finding the constant of proportionality from a graph?

Back

The constant of proportionality can be found by calculating the slope of the line, which is the change in y divided by the change in x.