About This Chapter
Linear Functions & Lines - Chapter Summary
In this fun chapter, our instructors discuss linear functions and lines, including the definition of a linear function and examples of this concept. You'll learn how to write and graph linear functions, as well as use the point-slope formula to find the equation of a line. Additional topics include graphing linear equations and the graphs of perpendicular and parallel lines in linear equations. Once you complete this chapter, you should be able to:
- Use the distance formula and the midpoint formula
- Calculate the angle formed from intersecting lines
- Give an example of division of intervals
- Define coordinate geometry and its associated formulas
Our short video and text lessons are designed by professional instructors to ensure your study experience is enjoyable. Each lesson is accompanied by a multiple-choice quiz you can use to test your understanding or to get ready for a class exam. If you struggle with any of the topics, feel free to contact one of our professional instructors for assistance.
1. What is a Linear Function? - Definition & Examples
In this lesson, you will learn the key identifying mark of linear functions. You'll also learn how to graph them with just two points and how you can use the graph to easily find your answers.
2. Writing & Graphing Linear Functions
We can show the relationship between two variables using a table, a graph or an equation. In this lesson, you will learn how to write and graph linear functions.
3. Equation of a Line Using Point-Slope Formula
It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.
4. Linear Equations: Intercepts, Standard Form and Graphing
Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.
5. Graphs of Parallel and Perpendicular Lines in Linear Equations
When we deal with linear equations, we sometimes come across equations that are parallel to each other or perpendicular to each other. You will see what they look like when graphed in this video lesson.
6. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
7. How to Use The Midpoint Formula
The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.
8. Calculating the Angle Formed From Intersecting Lines
In this lesson, you'll learn a different way of finding an angle between two intersecting lines. This method is useful when you know only the slopes of the lines.
9. Coordinate Geometry: Definition & Formulas
In this lesson we'll define coordinate geometry and learn about formulas that are commonly used in coordinate geometry. You can then take a brief quiz to see what you learned.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards