8th 4.6 PS

Front

What is a linear relationship?

Back

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).

Front

What does 'rate of change' mean in a linear relationship?

Back

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.

Front

What is the 'initial value' in a linear equation?

Back

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.

Front

How do you find the total cost in a linear relationship?

Back

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

Front

If a machine costs $75 to rent plus $8 per hour, what is the total cost for 5 hours?

Back

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

Front

What is the formula to calculate the initial value from a linear equation?

Back

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

Front

If the population increases by 142 people each year, what is the rate of change?

Back

The rate of change is 142 people per year.

Front

How do you interpret the initial value in a real-world context?

Back

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.

Front

What is the significance of the slope in a linear graph?

Back

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.

Front

If a painter charges $35 per hour and the total cost after 20 hours is $840, what is the initial value?

Back

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