Direct & Inverse 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 inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

If y varies directly with x and y = 84 when x = 16, what is the constant of variation (k)?

Back

k = y/x = 84/16 = 5.25.

Front

Write the equation for direct variation when y = 5.25 and x = 1.

Back

y = 5.25x.

Front

If the width of a rectangle varies inversely with its length and the width is 6 when the length is 24, what is the constant of variation (k)?

Back

k = width × length = 6 × 24 = 144.

Front

Write the equation for inverse variation when k = 144 and length = x.

Back

width = 144/x.

Front

If Daniel received $55.35 in interest on $1230, how do you find the interest for a different amount deposited?

Back

Use the formula: Interest = (Amount Deposited / Original Amount) × Original Interest.

Front

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

Back

y = kx², where k is the constant of variation.

Front

If y = 40 when x = 4 in a direct variation with the square of x, what is y when x = 7?

Back

y = kx²; k = 40/16 = 2.5; y = 2.5(7²) = 122.5.

Front

What does it mean for y to be directly proportional to the square of z and inversely proportional to w?

Back

It means y = k(z²/w), where k is a constant.