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

Front

What is the definition of 'constant rate of change'?

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity over time, often represented as a linear relationship.

Front

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

Back

The rate of change can be identified by calculating the slope of the line on the graph, which is the change in the y-values divided by the change in the x-values.

Front

What does a linear relationship look like on a graph?

Back

A linear relationship appears as a straight line on a graph, indicating a constant rate of change between the two variables.

Front

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

Back

The formula for slope is given by: \( m = \frac{{y2 - y1}}{{x2 - x1}} \)

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, such as speed, cost per item, or profit per hour.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is given by: \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.

Front

How can you determine the y-intercept from a linear equation?

Back

The y-intercept can be determined from the equation \( y = mx + b \) as the value of \( b \), which is the point where the line crosses the y-axis.

Front

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

Back

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

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change from a table, calculate the difference in the y-values divided by the difference in the x-values for two points.

Front

What is an example of a real-world situation that can be modeled with a linear equation?

Back

An example is calculating the total cost of items purchased, where the cost per item is constant.