3.2 Linear vs. Nonlinear

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not graph to a straight line, which can include curves, parabolas, and other shapes.

Front

What is the difference between discrete and continuous data?

Back

Discrete data consists of distinct, separate values (e.g., number of students), while continuous data can take any value within a range (e.g., height, weight).

Front

Give an example of a linear function.

Back

The function f(x) = 2x + 3 is a linear function because it can be represented by a straight line.

Front

Give an example of a nonlinear function.

Back

The function f(x) = x^2 is a nonlinear function because it graphs to a parabola.

Front

What does it mean for data to be discrete?

Back

Discrete data can only take specific values and cannot be divided into smaller parts.

Front

What does it mean for data to be continuous?

Back

Continuous data can take any value within a given range and can be measured in infinitely small increments.

Front

How can you identify a linear relationship in a real-life scenario?

Back

A linear relationship can be identified if the change in one variable results in a constant change in another variable, such as distance traveled over time at a constant speed.

Front

What is the slope in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0, indicating where the line crosses the y-axis.