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

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you determine the slope from a graph?

Back

The slope can be determined by finding the rise over run between two points on the line. It is calculated as (change in y) / (change in x).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

How can you identify a linear relationship from a table of values?

Back

A linear relationship can be identified if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change in real-world applications, such as speed, cost per item, or any quantity that changes at a constant rate.

Front

How do you write an equation from a given slope and y-intercept?

Back

To write an equation from a given slope (m) and y-intercept (b), use the slope-intercept form: y = mx + b.

Front

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

Back

The formula for calculating the slope (m) between two points is m = (y2 - y1) / (x2 - x1).