# Introduction to the Constant of Proportionality

## Opening

# Introduction to the Constant of Proportionality

Look at the table you completed comparing the dimensions of the real Empire State Building with those of the miniature building.

- What is the constant ratio in the table?

The constant ratio in a proportional relationship is called the *constant of proportionality*.

You can use the constant of proportionality to write a formula that represents the relationship between the quantities that vary.

- Let
*m*be the height of the miniature. - Let
*r*be the height of the real building.

The formula that represents the proportional relationship between the dimensions of the real building and the miniature building is *r *= 20*m*.

The 20 in the formula is the constant of proportionality.

The formula for a proportional relationship has the form

*y* = *kx*

where *k* is the constant of proportionality.

INTERACTIVE: Introducting the Constant of Proportionality