About This Chapter
Graphing on the Coordinate Plane - Chapter Summary
If you need a refresher on how to graph and interpret numerical data represented in the form of lines, parabolas or cubic polynomials, check out the video lessons included in this chapter. Use them to prepare for the math portion of the CAHSEE and learn how to:
- Determine the slope and intercepts of a line
- Graph lines with zero and undefined slopes
- Identify parallel and perpendicular lines
- Apply distance and midpoint formulas
- Write quadratic equations in various forms
- Graph cubic, quartic and quintic functions
- Solve and graph a system of linear equations
- Graph and interpret quantitative relationships
This chapter on graphing and the coordinate plane puts video lessons, transcripts and links to corresponding text lessons at your disposal. You can view and review content. There are even multiple-choice quizzes attached to the end of each lesson. When used together, these resources can help you find out what's on the CAHSEE, assess which areas require further study and map out a study plan.
Graphing on the Coordinate Plane - Objectives
Passing scores on the math portion of the CAHSEE are among the requirements for high school graduation in California. You can use this chapter's video lessons and quizzes to prepare for the test's Algebra and Functions section. It includes 17 multiple-choice questions, which comprise around 20% of exam content. You might be presented with a graph and asked to interpret the quantitative relationships between variables like speed, distance, time and cost. You could also be asked to identify the correct graph when given formulas for various polynomial functions.
1. How to Find and Apply The Slope of a Line
In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.
2. How to Find and Apply the Intercepts of a Line
How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.
3. Graphing Undefined Slope, Zero Slope and More
There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!
4. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
5. 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!
6. 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.
7. Graphing and Analyzing Quantitative Relationships
Sometimes your quantitative data will show a relationship when you graph it. If this is the case, then you can often times find an equation that represents your data by analyzing your graph.
8. Graphing Quantity Values With Constant Ratios
In this video lesson, you will see what the graph looks like when all your points have the same y:x or x:y ratio. You'll also learn how to write the equation of such a graph.
9. Interpreting Systems of Linear Equations Graphically
Graphing a system of linear equations is one way to find the solution of the system. Graphing the system out also lets you see if there is no solution at all.
10. What is a Parabola?
A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.
11. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
12. How to Graph Cubics, Quartics, Quintics and Beyond
Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!
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Other chapters within the CAHSEE Math Exam: Test Prep & Study Guide course
- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Algebraic Linear Equations & Inequalities
- Problems with Exponents
- Overview of Functions
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Matrices & Absolute Value
- Quadratics & Polynomials
- Geometry: Graphing Basics
- Measurement in Math
- Properties of Shapes
- Triangles, the Pythagorean Theorem & Congruency
- Perimeter, Area & Volume in Geometry
- Statistics, Probability & Working with Data
- Mathematical Reasoning
- Basic Mathematical Logic
- CAHSEE Math Exam Flashcards