Rate of Change

Front

What is the formula to calculate the slope of a line between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

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

Back

The slope represents the rate of change between two variables, indicating how much one variable changes in relation to another.

Front

If a line has a slope of 0, what does this indicate about the relationship between the two variables?

Back

A slope of 0 indicates that there is no change in the y-value as the x-value changes; the line is horizontal.

Front

What does a positive slope indicate about the relationship between two variables?

Back

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

Front

What does a negative slope indicate about the relationship between two variables?

Back

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

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

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

Back

To find the rate of change from a graph, select two points on the line, and use the slope formula: (change in y) / (change in x).

Front

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

Back

The y-intercept indicates the value of y when x is 0, providing a starting point for the line on a graph.

Front

How can you determine if a function is increasing or decreasing based on its slope?

Back

If the slope is positive, the function is increasing; if the slope is negative, the function is decreasing.

Front

What is the rate of change of a constant function?

Back

The rate of change of a constant function is 0, as there is no change in the output value regardless of the input.