Representing Ratios with Equations

Front

What is a ratio?

Back

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

How can ratios be represented?

Back

Ratios can be represented in three ways: as a fraction, with a colon (e.g., 2:3), or with the word 'to' (e.g., 2 to 3).

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What does the equation y = kx represent in a ratio context?

Back

In this equation, y is directly proportional to x, where k is the constant of proportionality.

Tags

CCSS.7.RP.A.2C

Front

If y = 18x, what does this tell us about the relationship between y and x?

Back

For every 1 unit increase in x, y increases by 18 units.

Tags

CCSS.HSF-LE.A.1B

Front

What does the coordinate point (2,10) represent in a ratio context?

Back

It means that for every 2 units of x, there are 10 units of y.

Tags

CCSS.7.RP.A.2C

Front

How do you find the constant of proportionality in a ratio?

Back

Divide y by x (k = y/x) to find the constant of proportionality.

Tags

CCSS.7.RP.A.2B

Front

What is the equation for a direct variation?

Back

The equation for direct variation is y = kx, where k is a non-zero constant.

Front

If Greg earns $6 per hour, how would you express his earnings as an equation?

Back

m = 6h, where m is the money earned and h is the hours worked.

Tags

CCSS.6.EE.C.9

Front

What is the meaning of the slope in a graph representing a ratio?

Back

The slope represents the rate of change between the two quantities being compared.

Tags

CCSS.8.EE.B.5

Front

How do you interpret the equation y = 2x?

Back

For every 1 unit increase in x, y increases by 2 units.

Tags

CCSS.HSF.LE.B.5