7.4A & 7.7A Constant Rate of Change & Linear Relationships

Front

What is a constant rate of change?

Back

A constant rate of change is a consistent amount that a quantity increases or decreases over a specific interval. In linear relationships, this is represented by the slope of the line.

Front

How do you find the slope of a line on a graph?

Back

The slope (rate of change) can be found by selecting two points on the line, calculating the difference in the y-values (rise) and the difference in the x-values (run), and then dividing rise by run.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate at which one quantity changes in relation to another. For example, in a graph showing distance over time, the slope indicates speed.

Front

What is the equation of a linear relationship?

Back

Front

What is the y-intercept in a linear equation?

Back

Front

How can you determine if a relationship is linear?

Back

A relationship is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

Front

What is the significance of the slope in a graph of a real-world scenario?

Back

The slope provides insight into the relationship between the variables, such as speed, cost per item, or growth rate.