Alg Module 13 Flashcard

Front

What does the slope in a linear regression equation represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable. For example, in the equation y = 1.5x + 12, the slope of 1.5 means that for each additional unit of x, y increases by 1.5.

Front

What are residuals in the context of linear regression?

Back

Residuals are the differences between the observed values and the values predicted by the regression model. They indicate how well the model fits the data.

Front

How do you calculate the value of a depreciating asset after a certain number of years?

Back

To calculate the value of a depreciating asset, use the formula: Value = Initial Value * (1 - Depreciation Rate)^Number of Years. For example, a car costing $27,000 with a 20% annual depreciation will be worth approximately $8,847.36 after 5 years.

Front

What type of function is characterized by a rapid increase or decrease?

Back

Exponential functions are characterized by rapid growth (exponential growth) or rapid decline (exponential decay).

Front

In an exponential function, what does the 'a' represent?

Back

In an exponential function of the form y = a * b^x, 'a' represents the y-intercept, which is the value of y when x = 0.

Front

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

Back

The formula for calculating the slope (m) of a line between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster increases over time.

Front

What does a positive slope indicate in a linear equation?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

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 the dependent variable when the independent variable is zero.