8th 4.6 PS

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation: y = mx + b, where m is the slope (rate of change) and b is the y-intercept (initial value).

The rate of change in a linear relationship refers to how much one variable changes in relation to another variable. It is represented by the slope (m) in the equation y = mx + b.

The initial value is the value of the dependent variable when the independent variable is zero. It is represented by the y-intercept (b) in the equation y = mx + b.

To find the total cost in a linear relationship, use the formula: Total Cost = Initial Value + (Rate of Change × Number of Units).

Total Cost = 75 + (8 × 5) = 75 + 40 = $115.

The initial value can be calculated using the formula: Initial Value = Total Cost - (Rate of Change × Number of Units).

The rate of change is 142 people per year.

The initial value represents the starting point or baseline amount before any changes occur. For example, it could represent the initial number of people, dollars, or items before any additions.

The slope indicates the steepness of the line and the direction of the relationship. A positive slope means an increase, while a negative slope indicates a decrease.

Initial Value = Total Cost - (Rate of Change × Number of Hours) = 840 - (35 × 20) = 840 - 700 = $140.