Representing Ratios with Equations

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as a fraction or with a colon (e.g., 3:2).

Front

How can ratios be represented using equations?

Back

Ratios can be represented using equations by expressing one quantity in terms of another, such as y = kx, where k is a constant that represents the ratio.

Front

What does the equation y = 5x represent in a real-world context?

Back

This equation indicates that for every car washed (x), $5 is earned (y). It shows a direct proportional relationship between the number of cars washed and the total money earned.

Front

If t = 10d, what does this equation mean?

Back

This equation means that for every unit of d (e.g., distance), t (e.g., time) is 10 times that amount, indicating a direct proportional relationship.

Front

What is the significance of the slope in the equation y = mx?

Back

The slope (m) represents the rate of change between the two variables, indicating how much y changes for a unit change in x.

Front

How do you find the total money earned if the equation is m = 6h?

Back

To find the total money earned (m), multiply the number of hours worked (h) by the hourly rate (6). For example, if h = 9, then m = 6 * 9 = $54.

Front

What does the equation y = 400x represent?

Back

This equation indicates that for every unit of x, y increases by 400, showing a direct proportional relationship.

Front

What is the formula to convert a ratio into a fraction?

Back

To convert a ratio a:b into a fraction, you can write it as a/b.

Front

What is a constant of proportionality?

Back

The constant of proportionality is the constant factor (k) in the equation y = kx that relates two proportional quantities.

Front

How can you determine if two quantities are proportional?

Back

Two quantities are proportional if their ratio remains constant as the quantities change.