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

If y varies directly with x and y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

If y = 13x, what is the value of y when x = 2?

Back

y = 13 * 2 = 26.

Front

What is the equation representing direct variation if y = 16 when x = 32?

Back

y = (1/2)x.

Front

Is the equation y = 2x a direct variation?

Back

Yes, it is a direct variation.

Front

If y is directly proportional to x and y = 10 when x = 3, what is the value of y when x = 5?

Back

y = (10/3) * 5 = 16 2/3.

Front

What does it mean for y to vary directly with x?

Back

It means that as x increases or decreases, y changes in a proportional manner.

Front

If y = kx, what happens to y if k is doubled?

Back

If k is doubled, y will also double for the same value of x.

Front

What is the graph of a direct variation equation like?

Back

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

Front

If y = 0 when x = 0, is this a direct variation?

Back

Yes, because it satisfies the condition of passing through the origin.