Chapter Outline

The Coordinate Plane

The coordinate plane is a tool for graphing algebraic relationships.

• It is divided by a horizontal line called the x-axis and a vertical line called the y-axis.
• The two lines intersect at 0, the origin.

A point anywhere on the plane can be identified by a pair of numbers called the coordinates of the point. The coordinates are written inside parentheses in the order (x,y).

• The x-coordinate is positive for numbers to the right of the vertical axis and negative for numbers to the left.
• The y-coordinate is positive for numbers above the horizontal axis and negative for numbers below.

On the GED Mathematics Test you will see coordinate plane grids with small circles where you can mark the position of a point.

To find the distance between points on the coordinate plane, you can sometimes count spaces.

The formula for finding the distance between any two points on the coordinate plane is based on the Pythagorean relationship.

Linear Equations

The graph of a linear equation forms a straight line.

Slope and Intercepts

The slope is a measure of how "steep" a line is.

• A line that rises from left to right has a positive slope.
• A line that goes down from left to right has a negative slope.
• A horizontal line has zero slope.
• A vertical line is said to have an undefined slope.
• The slope of a line is (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.

An intercept tells where a line crosses an axis.

• To find the y-intercept of a linear equation, substitute 0 for x and solve for y.

Multiplying and Dividing Monomials

To multiply monomials, follow these steps:

• Follow the rules for multiplying signed numbers.
• Add the exponents of like variables.
• Remember that a variable with no exponent is understood to be to the first power.

To divide monomials, follow these steps:

• Follow the rules for dividing signed numbers.
• Subtract the exponents of like variables.

Factoring

Factoring means writing a number or an expression as a product of other numbers or terms.

A number that has an exact square root is called a perfect square. For some numbers, one factor is a perfect square. To simplify a square root, follow these steps:

• Find a factor that is a perfect square.
• Write the square root of the perfect square outside the √ sign and leave the other factor inside the √ sign.

Trigonometric Ratios

Trigonometry is the study of the relationship between pairs of sides in right triangles. There are three common ratios in trigonometry:

• The sine of an angle is the ratio of the length of the opposite side of the triangle to the length of the hypotenuse.
• The cosine of an angle is the ratio of the length of the adjacent side of the triangle to the length of the hypotenuse.
• The tangent of an angle is the ratio of the length of the opposite side of the triangle to the length of the adjacent side of the triangle.

Quadratic Equations

• In a quadratic equation a variable is raised to the second power.
• The graph of a quadratic equation is called a parabola.