Linear Functions
Slope, intercepts, and linear equations
Start with the basics and progress through 7 lessons. Each lesson builds on the previous one.
0 of 7 lessons done
Test Your Knowledge
10 questions, new mix each time (from 120)
In This Topic (7 lessons)
Introduction to Linear Functions
Learn what linear functions are, how to identify them, and how they create straight lines on a graph.
Slope-Intercept Form (y = mx + b)
Learn to write, graph, and interpret linear equations in slope-intercept form, the most useful form for understanding how lines behave.
Understanding Slope
Learn what slope means, how to calculate it, and why it's essential for describing linear relationships.
Point-Slope Form
Learn how to write and use the point-slope form of a linear equation when you know a point and the slope.
Standard Form of Linear Equations
Learn to write and interpret linear equations in standard form Ax + By = C.
Writing Linear Equations
Learn to write linear equations from given information like slope, points, or real-world situations.
Parallel and Perpendicular Lines
Learn how to identify parallel and perpendicular lines using their slopes, and write equations for lines with these special relationships.
Linear functions are the foundation of mathematical modeling. A linear function creates a straight line when graphed and represents a constant rate of change. From calculating costs to predicting trends, linear functions appear everywhere in science, business, and daily life. Understanding them opens the door to all higher mathematics.
In this topic, you will explore linear functions through multiple representations: tables, graphs, equations, and verbal descriptions. You will master slope as a measure of steepness and rate of change, and y-intercept as the starting point. Different forms of linear equations—slope-intercept, point-slope, and standard form—each reveal different aspects of the function.
Our interactive lessons help you see connections between representations and build intuition for how changing parameters affects the graph. You will write equations from graphs and real-world scenarios, interpret slopes and intercepts in context, and use linear functions to make predictions.
What You'll Learn
- Calculate slope from two points or a graph
- Write linear equations in slope-intercept form (y = mx + b)
- Convert between slope-intercept, point-slope, and standard forms
- Graph linear functions using slope and y-intercept
- Interpret slope and y-intercept in real-world contexts
- Write equations from graphs or word problems
- Identify parallel and perpendicular lines by slope
Frequently Asked Questions
What does slope represent?
Slope measures the steepness of a line and the rate of change. It tells you how much y changes for each unit increase in x. A slope of 3 means y increases by 3 for every 1 unit increase in x.
What is the y-intercept?
The y-intercept is where the line crosses the y-axis (when x = 0). In y = mx + b, the value b is the y-intercept. It often represents a starting value or fixed cost in real problems.
When should I use each form of a linear equation?
Use slope-intercept (y = mx + b) for quick graphing. Use point-slope (y - y₁ = m(x - x₁)) when you have a point and slope. Use standard form (Ax + By = C) for certain applications and integer coefficients.