8.5B-Non-Proportional Linear Relationships

Front

What is a non-proportional linear relationship?

Back

A non-proportional linear relationship is a relationship between two variables that can be represented by a linear equation, but does not pass through the origin (0,0). This means that the y-intercept is not zero.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes.

Front

How do you calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (change in y) over the run (change in x).

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept can represent the starting value of a situation in real-world applications, such as the initial cost before any changes occur.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships pass through the origin (0,0) and have a constant ratio, while non-proportional relationships do not pass through the origin and have a y-intercept that is not zero.