Constant Rate of Change with Tables/Graphs/Equations

Front

What is a constant rate of change?

Back

A constant rate of change refers to a situation where a quantity changes at a consistent rate over time, represented by a straight line on a graph.

Front

How can you identify a constant rate of change in a graph?

Back

A constant rate of change can be identified in a graph by a straight line, indicating that the change in the y-value is consistent for each unit change in the x-value.

Front

What does a slope of a line represent in the context of rate of change?

Back

The slope of a line represents the rate of change, calculated as the rise (change in y) over the run (change in x).

Front

If a graph shows a slope of 2, what does this indicate?

Back

A slope of 2 indicates that for every 1 unit increase in x, the y-value increases by 2 units.

Front

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

Back

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

Front

How do you interpret a graph that shows a linear relationship?

Back

A linear relationship in a graph indicates that as one variable increases or decreases, the other variable does so at a constant rate.

Front

What does it mean if a graph is not linear?

Back

If a graph is not linear, it indicates that the rate of change is not constant, and the relationship between the variables may be quadratic, exponential, or another non-linear form.

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 determine the rate of change from a table of values?

Back

To determine 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 does a rate of 500 earned for every 8 hours worked imply?

Back

This implies that for every 8 hours of work, an individual earns $500, which can be expressed as a rate of $62.50 per hour.