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 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 = 2, what is the value of k?

Back

k = 10/2 = 5.

Front

What is the graph of a direct variation relationship?

Back

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

Front

If y varies directly with x and y = 15 when x = 3, what is y when x = 5?

Back

y = kx; k = 15/3 = 5; y = 5 * 5 = 25.

Front

What does it mean if two quantities vary inversely?

Back

Two quantities vary inversely if one quantity increases while the other decreases, and their product is constant. This can be expressed as y = k/x.

Front

If x and y vary inversely and k = 30, what is y when x = 6?

Back

y = k/x; y = 30/6 = 5.

Front

What is an example of direct variation in real life?

Back

An example of direct variation is the relationship between the distance traveled and the time taken at a constant speed.

Front

What is the relationship between the variables in an inverse variation?

Back

In inverse variation, as one variable increases, the other variable decreases, maintaining a constant product.

Front

If y varies directly with x and y = 8 when x = 4, what is the equation of the variation?

Back

The equation is y = 2x.