DIRECT VARIATION

Front

What is Direct Variation?

Back

Direct Variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is a non-zero constant.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a direct variation, where y varies directly with x. The constant k is the constant of variation.

Front

If y = 12 when x = 3, what is the value of k?

Back

k = 4 (since y = kx, 12 = k(3) => k = 12/3 = 4).

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

Slope = 2 (calculated as (6-2)/(3-1) = 4/2 = 2).

Front

What is the slope of a line in direct variation?

Back

The slope of a line in direct variation is equal to the constant of variation (k).

Front

If y = 20 when x = 5, find y when x = 10.

Back

y = 40 (since k = 4, y = kx => y = 4(10) = 40).

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, as x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

If y = 15 when x = 3, what is y when x = 6?

Back

y = 30 (since k = 5, y = kx => y = 5(6) = 30).

Front

What does it mean if two variables are directly proportional?

Back

If two variables are directly proportional, it means that they maintain a constant ratio to each other.

Front

Find the value of y when x = 4 if y = 8 when x = 2.

Back

y = 16 (since k = 4, y = kx => y = 4(4) = 16).