Writing Function Rules from Tables

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from a table of values?

Back

The slope can be determined by taking the difference in the y-values divided by the difference in the x-values between two points.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can you write a function rule from a table of values?

Back

Identify the pattern in the changes of x and y values, then express this relationship as an equation.

Front

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

Back

The slope indicates the rate of change of the function; it shows how much y changes for a unit change in x.

Front

What does it mean if a function is linear?

Back

A linear function is one that graphs to a straight line, meaning it has a constant rate of change.

Front

How can you verify if an equation matches a table of values?

Back

Substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

What is the general form of a linear equation?

Back

The general form is Ax + By = C, where A, B, and C are constants.

Front

What is the relationship between the coefficients in the equation y = mx + b?

Back

The coefficient m represents the slope, while b represents the y-intercept of the line.