# Ch 2: Saxon Algebra 2: Graphs on the Coordinate Plane

### About This Chapter

## How It Works:

- Identify the lessons in the Saxon Graphs on the Coordinate Plane chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the graphs topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- The distance formula
- Graphing by substitution
- Calculating the slope of a line
- Horizontal and vertical lines
- Parallel and perpendicular lines
- Graphing circles and elipses
- Hyperbolas and parabolas
- Systems of equations
- Y-intercepts
- Graphing linear equations

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. How to Use The Distance Formula

The distance formula is a shortened form of the Pythagorean Theorem. Learn about the Pythagorean Theorem and the distance formula, along with examples of how the formula is used.

### 2. How to Graph Linear Equations by Substitution

Linear equation graphs are always straight lines, so substitution can be an easy way to draw the graph. In this lesson, we'll explore how to find and use the points you need, so graphing linear equations can be easy!

### 3. What is a System of Equations?

Math word problems often ask students to compare and contrast, which are types of problems that can be solved with a system of equations. Learn about solving word problems using systems of equations and how to graph them, as well as the algebraic method of substitution through an example.

### 4. What is Slope? - Definition & Formulas

The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points. Learn how to calculate the slope of a line and how to find a slope on a Cartesian plane.

### 5. Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

Calculating the slope of a line means finding out how steep the line is and if it is uphill or downhill. Study the point-slope form, slope-intercept form, and learn how to find the slope of parallel and perpendicular lines.

### 6. Y-Intercept: Definition & Overview

In this lesson, you will learn about the y-intercept, a particular point (or several points) on a graph where the line or curve touches or crosses the y-axis.

### 7. What are Horizontal Lines? - Definition & Equations

A horizontal line is a straight line that is parallel to the x-axis. Learn about the definition and examples of horizontal lines and find out the slope, equation, and graph of a horizontal line.

### 8. Vertical Line: Equation & Slope

A vertical line is a straight line that is parallel to the y-axis and is always represented by an x in an equation. Learn how to prove that a vertical line has no slope, or gradient, by trying to calculate it.

### 9. Graphs of Parallel and Perpendicular Lines in Linear Equations

Linear equations, which are graphed as straight lines, can have associated parallel lines which never touch, and perpendicular lines that intersect at 90 degrees. Learn the equations and see the graphs of these two types of linear equations.

### 10. How to Graph Consistent, Inconsistent & Dependent Linear Equations

When two linear equations are graphed on the x,y coordinate grid, you have three possible results. The two equations can be consistent, inconsistent, or dependent. This lesson explains how to graph these equations and what the graphs mean.

### 11. Graphing Circles: Identifying the Formula, Center and Radius

Graphing a circle requires knowing the center, radius, and circle formula. Changing the exponents in the formula changes the size and location on the graph. Learn how to to correctly graph a circle by identifying the formula, center, and radius.

### 12. Defining and Graphing Ellipses in Algebra

An ellipse is a circle that has been stretched, with the horizontal path from the radius shorter than the vertical. Learn how to define the ellipse, and how the equation is used in the graphing of ellipses in algebra.

### 13. The Hyperbola: Definition, Vertices, Foci & Graphing

The standard equation of a hyperbola can be used to identify its vertices and foci for graphing. Learn the definition and standard equation of a hyperbola, understand how to identify its vertices and foci, and practice graphing with an example.

### 14. The Parabola: Definition & Graphing

In mathematics, a parabola is a u-shaped figure that looks similar to an arc. Learn about the definition, standard form equation, and how to graph a horizontal/vertical parabola.

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### Other Chapters

Other chapters within the Saxon Algebra 2 Homeschool: Online Textbook Help course

- Saxon Algebra 2: Decimal Numbers
- Saxon Algebra 2: Sets
- Saxon Algebra 2: Real Numbers
- Saxon Algebra 2: Complex Numbers
- Saxon Algebra 2: Conversion by Unit Multipliers
- Saxon Algebra 2: Ratio & Proportion
- Saxon Algebra 2: Percent
- Saxon Algebra 2: Rate
- Saxon Algebra 2: Exponents
- Saxon Algebra 2: Exponents on a Scientific Calculator
- Saxon Algebra 2: Roots
- Saxon Algebra 2: Probability
- Saxon Algebra 2: Statistics
- Saxon Algebra 2: Simplifying Expressions
- Saxon Algebra 2: Polynomials
- Saxon Algebra 2: Simplifying Rational Expressions
- Saxon Algebra 2: Simplifying and Solving Equations
- Saxon Algebra 2: Linear Equations
- Saxon Algebra 2: Solving Linear Equations
- Saxon Algebra 2: Quadratic Equations
- Saxon Algebra 2: Other Types of Equations
- Saxon Algebra 2: Understanding Functions
- Saxon Algebra 2: Manipulating and Evaluating Functions
- Saxon Algebra 2: Trigonometry
- Saxon Algebra 2: Logarithms
- Saxon Algebra 2: Lines, Points, Segments, and Planes
- Saxon Algebra 2: Angles
- Saxon Algebra 2: Polygons
- Saxon Algebra 2: Circles
- Saxon Algebra 2: Triangles
- Saxon Algebra 2: Geometric Solids
- Saxon Algebra 2: Perimeter and Circumference
- Saxon Algebra 2: Area
- Saxon Algebra 2: Surface Area and Volume
- Saxon Algebra 2: Constructions
- Saxon Algebra 2: Postulates & Pythagorean Theorem
- Saxon Algebra 2: Proofs