Semester Exam Review

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the amount by which the dependent variable (e.g., balance) changes for each unit increase in the independent variable (e.g., number of deposits). It is often represented as the slope of the line.

Front

How do you calculate the slope of a line given two points?

Back

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

Front

What is the equation of a linear function?

Back

A linear function can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x = 0. It represents the point where the line crosses the y-axis.

Front

What does the x-intercept represent in a linear equation?

Back

The x-intercept is the value of x when y = 0. It represents the point where the line crosses the x-axis.

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What does it mean for a graph to be shifted vertically?

Back

A vertical shift occurs when a constant is added to or subtracted from the function's output, moving the graph up or down without changing its shape.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

How do you interpret the slope of a linear function in a real-world context?

Back

In a real-world context, the slope represents the rate of change between two quantities, such as cost per item or speed.

Front

What is the relationship between two functions if one is derived from the other by a vertical shift?

Back

If one function is derived from another by a vertical shift, it means that the graphs of the two functions are identical in shape but differ in their vertical position.