Constant Rate of Change/ Constant of Proportionality

The formula is $$y = kx$$ , where y is the dependent variable, k is the constant of proportionality, and x is the independent variable.

The constant of proportionality can be found by dividing the dependent variable by the independent variable, i.e., $$k = \frac{y}{x}$$ .

$$\frac{450}{300} = 1.5 in.$$ , so 1 spring requires 1.5 inches of wire.

A constant rate of change represents a straight line in a graph, indicating that as one variable increases, the other variable increases at a consistent rate.

The constant of proportionality is $$k = \frac{2.50}{10} = 0.25$$ , meaning each ticket costs $0.25.

The relationship can be expressed as $$y = kx$$ , where y is the total cost, k is the cost per item, and x is the number of items.

The equation is $$y = 4.25x$$ .

A proportional relationship means that two quantities maintain a constant ratio to each other.

A relationship is proportional if the ratio of y to x is constant for all pairs of values.

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