Modeling Linear Functions

Front

What is a linear function?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that they intersect at a right angle.

Front

What is a residual in the context of linear regression?

Back

A residual is the difference between the observed value and the predicted value of the dependent variable. It measures the error of the prediction.

Front

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

Back

Front

What is the y-intercept of a linear function?

Back

Front

How do you determine if a line is increasing or decreasing?

Back

A line is increasing if its slope is positive (m > 0) and decreasing if its slope is negative (m < 0).

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Back

Front

What is the significance of the correlation coefficient?

Back

The correlation coefficient measures the strength and direction of a linear relationship between two variables. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation.