Constant of Proportionality (Graphs)

Front

What is the definition of the constant of proportionality?

Back

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

Tags

CCSS.7.RP.A.2B

Front

How do you identify the constant of proportionality in an equation?

Back

The constant of proportionality can be identified as the coefficient of x in the equation y = kx.

Tags

CCSS.7.RP.A.2C

Front

If y = 5x, what is the constant of proportionality?

Back

The constant of proportionality is 5.

Tags

CCSS.7.RP.A.2B

Front

What is the relationship between the constant of proportionality and the slope of a graph?

Back

In a graph of y = kx, the constant of proportionality (k) represents the slope of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How does changing the constant of proportionality affect the graph of the equation y = kx?

Back

Changing the constant of proportionality alters the steepness of the line; a larger k results in a steeper line, while a smaller k results in a flatter line.

Tags

CCSS.8.EE.B.5

Front

What does it mean if the constant of proportionality is negative?

Back

If the constant of proportionality is negative, the graph of the equation y = kx will slope downwards from left to right.

Tags

CCSS.8.EE.B.5

Front

Can the constant of proportionality be zero? What does it represent?

Back

Yes, if the constant of proportionality is zero, the equation becomes y = 0, which represents a horizontal line on the graph.

Tags

CCSS.8.EE.B.5

Front

How can you determine the constant of proportionality from a table of values?

Back

To determine the constant of proportionality from a table, divide the value of y by the corresponding value of x for any pair of values.

Tags

CCSS.7.RP.A.2B

Front

What is the significance of the constant of proportionality in real-world applications?

Back

The constant of proportionality helps to understand the relationship between two quantities, such as speed, density, or cost per item.

Tags

CCSS.7.RP.A.2B

Front

If the constant of proportionality is 3, what is the value of y when x = 4?

Back

If k = 3 and x = 4, then y = 3 * 4 = 12.

Tags

CCSS.7.RP.A.2B