7.4A Constant Rate of Change

Front

What is a constant rate of change?

Back

A constant rate of change is a consistent amount of change in a quantity over a specific period of time, often represented as a slope in a graph.

Front

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

Back

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

Front

What is the formula for calculating the slope (rate of change)?

Back

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

Front

If a graph shows a straight line, what does that indicate about the rate of change?

Back

A straight line indicates a constant rate of change, meaning the relationship between the two variables is linear.

Front

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

Back

In a real-world context, the slope represents the rate at which one quantity changes in relation to another, such as speed, cost per item, or growth rate.

Front

How can you determine the equation of a line from a graph?

Back

To determine the equation of a line, identify the slope and the y-intercept from the graph, then use the slope-intercept form y = mx + b.

Front

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

Back

The y-intercept is the value of y when x is 0, representing the starting point of the relationship on a graph.

Front

If JoAnne deposits $150 in 3 months, what is her constant rate of change?

Back

Her constant rate of change is $50 per month, calculated as ($300 - $150) / (6 - 3) = $50.

Front

What does a steeper slope indicate about the rate of change?

Back

A steeper slope indicates a greater rate of change, meaning the dependent variable changes more rapidly with respect to the independent variable.

Front

How do you write an equation from a table of values?

Back

To write an equation from a table, identify the rate of change (slope) and the starting value (y-intercept) to form the equation in the form y = mx + b.