Linear Functions Study Guide

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear function?

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 function is discrete or non-discrete?

Back

A function is discrete if it consists of distinct, separate values (like counting numbers). It is non-discrete if it can take any value within a range (like measurements).

Front

What is the constant of proportionality in a linear relationship?

Back

The constant of proportionality is the coefficient of x in the equation y = kx, where k represents the constant ratio between y and x.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values in the table.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If Adam earns $10 for each car he washes, what type of function does this represent?

Back

This represents a discrete function because the number of cars washed can only be whole numbers.

Front

What is the difference between discrete and continuous data?

Back

Discrete data consists of separate values (like counts), while continuous data can take any value within a range (like measurements).

Front

How do you express a linear relationship in the form y = kx?

Back

To express a linear relationship in the form y = kx, identify the constant ratio between y and x, where k is the constant of proportionality.