Direct variation and slopes

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 is the constant of variation in direct variation?

Back

The constant of variation (k) is the ratio of y to x in a direct variation relationship, represented as k = y/x.

Front

If y varies directly with x, and y = 10 when x = 5, what is the constant of variation?

Back

k = 10/5 = 2.

Front

What is the graph of a direct variation?

Back

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

Front

If x = 3 and y = 12 in a direct variation, what is the equation?

Back

y = 4x.

Front

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

Back

(0, 0).

Front

If y varies directly as x and y = 8 when x = 2, what is y when x = 4?

Back

y = 16.

Front

Is the relationship y = 3x a direct variation?

Back

Yes, because it can be expressed in the form y = kx.

Front

If y = 5 when x = 1, what is the equation of the direct variation?

Back

y = 5x.

Front

What does it mean if two variables do not vary directly?

Back

It means that the ratio of y to x is not constant.