TEKS 7.4 A-C (Constant Rate of Change)

Front

What is a 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. It is often represented by a linear function.

Front

How can you identify a linear function?

Back

A linear function can be identified by its constant rate of change, which means that the graph of the function is a straight line.

Front

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

Back

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

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 of change between two variables, such as speed (distance over time) or cost (price per item).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How do you find the y-intercept from a linear equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the y-intercept is represented by the value of b.

Front

What is the difference between positive and negative slope?

Back

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

Front

What is a proportional relationship?

Back

A proportional relationship is a type of linear relationship where the ratio of the two variables is constant, and the graph passes through the origin (0,0).

Front

How can you determine if a table of values represents a constant rate of change?

Back

To determine if a table of values represents a constant rate of change, calculate the differences between the y-values and the corresponding x-values. If the ratios are consistent, it indicates a constant rate of change.

Front

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

Back

The x-intercept is the point where the line crosses the x-axis, representing the value of x when y is 0.