Proportional, Linear, Rate of Change

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio, meaning that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What does it mean for a graph to be linear?

Back

A linear graph represents a relationship between two variables that can be expressed with a linear equation, resulting in a straight line when plotted on a coordinate plane.

Front

How do you determine the rate of change from a graph?

Back

The rate of change is determined by calculating the slope of the line, which is the change in the y-values divided by the change in the x-values (rise over run).

Front

What is the formula for calculating the slope of a line?

Back

The formula for calculating the slope (m) of a line is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as one variable increases, the other variable also increases, showing a direct relationship.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and is straight.

Front

What does the point (3, 27) represent in a real-world context?

Back

The point (3, 27) represents a scenario where 3 items (e.g., shirts) cost a total of $27, indicating a price of $9 per shirt.

Front

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

Back

Proportional relationships have a constant ratio and pass through the origin, while non-proportional relationships do not maintain a constant ratio and may not pass through the origin.