Algebra 1 4.4 Direct Variation Equation

Front

What is the definition of direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed as y = kx, where k is the constant of variation.

Front

What is the constant of variation in a direct variation equation?

Back

The constant of variation (k) is the non-zero constant that relates the two variables in a direct variation equation, indicating how much y changes for a unit change in x.

Front

What ordered pair does a direct variation always go through when graphed?

Back

(0, 0)

Front

If y varies directly with x, what is the equation form?

Back

y = kx

Front

How do you find the constant of variation from a direct variation problem?

Back

To find the constant of variation, divide y by x (k = y/x) when given a specific ordered pair.

Front

If a car travels 120 miles in 2 hours, what is the constant of variation (speed)?

Back

k = 60 miles per hour.

Front

What does the graph of a direct variation look like?

Back

The graph of a direct variation is a straight line that passes through the origin (0, 0).

Front

If y = 3 when x = 9, what is the constant of variation?

Back

k = 1/3.

Front

What is the relationship between x and y in the equation y = 5x?

Back

y varies directly with x, with a constant of variation k = 5.

Front

Does the equation y = 2x + 3 represent direct variation?

Back

No, because it does not pass through the origin.