Topic 3: Linear Functions (enVision Algebra 1)

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the point where the graph of the function crosses the y-axis. It represents the value of f(x) when x = 0.

Front

How does a vertical translation affect the graph of a linear function?

Back

A vertical translation shifts the graph up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of a horizontal translation on a linear function?

Back

A horizontal translation shifts the graph left or right. If h is positive, the graph shifts left; if h is negative, it shifts right.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function f(x) at a specific point x = a, substitute a into the function and calculate f(a).

Front

What is the formula for finding the line of best fit?

Back

The line of best fit can be found using linear regression, which calculates the best-fitting line through a set of data points.

Front

What does a correlation coefficient of 0.99 indicate?

Back

A correlation coefficient of 0.99 indicates a very strong positive linear relationship between two variables.

Front

How do you interpret the slope of a line of best fit?

Back

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

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.