Algebra: Equations of Linear Functions

Front

What is a linear function?

Back

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you determine if a correlation is positive or negative from a scatter plot?

Back

A positive correlation means that as one variable increases, the other variable also increases. A negative correlation means that as one variable increases, the other variable decreases.

Front

What does a strong correlation indicate?

Back

A strong correlation indicates that there is a close relationship between two variables, meaning that changes in one variable are closely associated with changes in the other.

Front

What is the difference between correlation and causation?

Back

Correlation indicates a relationship between two variables, but it does not imply that one variable causes the other to change. Causation means that one variable directly affects the other.

Front

What does it mean if a linear function is increasing?

Back

An increasing linear function has a positive slope, meaning that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does it mean if a linear function is decreasing?

Back

A decreasing linear function has a negative slope, meaning that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is a residual plot?

Back

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps to assess the fit of a regression model.

Front

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

Back

The slope of a line of best fit represents the average change in the dependent variable for each unit change in the independent variable.