8.5 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

If y varies directly as x, and y = 12 when x = 5, what is the constant of variation (k)?

Back

k = y/x = 12/5 = 2.4.

Front

How do you find the value of y when x is given in direct variation?

Back

Use the formula y = kx, where k is the constant of variation.

Front

What is inverse variation?

Back

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

Front

If y varies inversely as x, and y = -3 when x = -6, what is the constant of variation (k)?

Back

k = y * x = -3 * -6 = 18.

Front

How do you find the value of y when x is given in inverse variation?

Back

Use the formula y = k/x, where k is the constant of variation.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is y = k/x.

Front

If the sales at a baseball game vary directly with the number of people attending, how do you calculate attendance if sales are known?

Back

Set up the equation using the direct variation formula: sales = k * attendance.

Front

If the width of a rectangle varies inversely with its length, how do you find the width when the length changes?

Back

Use the inverse variation formula: width = k/length, where k is the constant found from initial width and length.