Prerequisites

Most the material in this section was considered to be review and not directly covered by the teacher. The teacher did however go over how to write inequality statements in interval notation.
 * __P.1 Real Numbers__**

__Interval Notation:__ 1. Bounded Intervals a) Open: (a, b) b) Closed: [a, b] c) Half-open: (a, b] or [a, b)

2. Unbounded Intervals a) Open: (a, inf) b) Closed: (-inf, a]

Ex. Convert into interval notation: -3 <= x <5 Answer: [-3, 5)

The teacher did not specifically cover any material from this section.
 * __P.2 Cartesian Coordinate System__**

The teacher did not specifically cover any material from this section.
 * __P.3 Linear Equations and Inequalities__**

__**P. 4 Lines in the Plane** Slope__ = m = rise/run = (y2 - y1)/(x2 - x1) Ex. Find the equation of the line through these two points: (1, 5) and (2, 9) Answer: m = (9 - 5)/(2 - 1) = 4/1 = 4

__Point-Slope Form:__ y - y1 = m(x - x1)

__Slope-intercept Form:__ y = mx + b

__General Form:__ ax + by + c = 0 where a and b not both zero

__Parallel Lines__ have the same slope __Perpendicular Lines__ have opposite reciprocal slopes Ex. Find the equation of the line in general form that goes through (2, -4) and is perpendicualr to y = -2x + 10 Answer: slope of the new line is m = -2 y = -2x + b -4 = -2(2) + b -4 = -4 + b 0 = b Final answer: y = -2x

__Linear Regression:__ We can use our graphing calculator to make a scatter plot and use the linear regression feature to find the equation of the line of best fit.

We can solve equations using a graph in several ways: 1. Set the equation equal to zero and graph. Then, find where the graph crosses the x-axis with the table or calculate feature. 2. Graph the left side of the equation and graph the right side of the equation. Then, find where the graphs intersect using the calculate feature.
 * __P.5 Solving Equations Graphically, Numerically, and Algebraically__**

__Linear Equation in X:__ ax + b = 0 where a /= 0 __Quadratic Equation in X:__ ax^2 + bx + c = 0 where a /= 0

__Methods for solving Quadratic Equations:__ 1. Factoring (only works when factorable) 2. Square-root method (only works when you can isolate x^2) 3. Completing the square (always works) 4. Quadratic formula (always works)