Linear+Equations+and+Graphs

A **linear equation** is an algebric equations in which each term is either a constant or the product of a constant times the first power of a variable. Linear equations can have one, two, three or more variable.
 * Linear Equations**: a mathematical statement that performs functions of addition, subtraction, multiplication, and division.

> For example, //x// squared or //x// 2 > For example: "x" times "y" or xy; "x" divided by "y" or x/y > For example: Ö x or the "square root of x"; sqrt (x) (here an example) http://www.mathwarehouse.com/classroom/worksheets-and-activities.php Formulas and Equations:** **Graph** **linear equations(graph plotting)**
 * //variable(s)// in linear expressions**
 * Cannot have exponents (or powers)
 * Cannot multiply or divide each other
 * Cannot be found under a root sign or square root sign (sqrt)
 * Examples

**Graph of a linear equation

5 KEY TERMS OF A LINEAR EQUATION AND GRAPH

Y-Axis:** where //m// is the slope of the line and //b// is the //y//-intercept, which is the //y//-coordinate of the point where the line crosses the //y// axis.   **Formula: Y=MX+B

X-Axis:** where //m// is the slope of the line and //c// is the //x//-intercept, which is the //x//-coordinate of the point where the line crosses the //x// axis.
 * Formula: X=Y / M + C

Point Slope:** where //m// is the slope of the line and (//x//1,//y//1) is any point on the line. The point-slope and slope-intercept forms are easily interchangeable. The point-slope form expresses the fact that the difference in the //y// coordinate between two points on a line (that is, //y// − //y//1 ) is proportional to the difference in the //x// coordinate (that is, //x// − //x//1 ).
 * Formula:[[image:http://upload.wikimedia.org/math/a/2/1/a211b4370086efa422855a2d30c453a3.png caption="y - y_1 = m cdot ( x - x_1 ),"]]

Intercept:** where //c// and //b// must be nonzero. The graph of the equation has //x//-intercept //c// and //y//-intercept //b//.
 * Formula:[[image:http://upload.wikimedia.org/math/0/0/d/00d041dc875043a6476fd36a7a7ba0c8.png caption="frac{x}{c} + frac{y}{b} = 1"]]

Standard:** where //A//, //B//, and //C// are integers whose greatest common factor is 1, //A// and //B// are not both equal to zero and, //A// is non-negative (and if A=0 then B has to be positive).
 * Formula: [[image:http://upload.wikimedia.org/math/7/e/6/7e6859919d495035e99c333d04e3e0b9.png caption="Ax + By = C,,"]]

4 EXAMPLES:** 1. Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a month? (assume 4 weeks per month) (http://www.algebralab.org/practice/practice.aspx?file=Word_LinearEquations.xml) **To solve the problem you substitute the m for $40 and b for -$400. then find the value of x and plug it in. once the are all plug in, solve the equation. The answer should be $4400. Make sure to use the formula (y=mx+b).** **2.** John is starting a roofing business. He will need to buy a truck and some supplies to get his business going. The truck costs $13000 used. He gets three jobs right away. And hires 2 workers to help him. The materials for all three jobs cost $3000. The jobs will each take a week not including Saturday and Sunday and he pays his workers $125 per day per worker. How much will he have to charge for each job in order to break even at the end of the third job? **To solve the problem set up the equation like this:** Profit equals three jobs times the amount charged per job then take away expenses. Expenses would be the truck, the materials and the labor for all three jobs. ( ** The answer should be $6583.33). ** // x // + 1 - 1 = 4 - 1 Now simplifying both sides we have: // x // + 0 = 3 So: // x // =3 - 2//x// = 12 1. Divide both sides by -2: 2. Simplify both sides: // x // =  - 6
 * 3.** **another way to solve linear equations**
 * 4.** **solving for x**

**1 WORD PRPBLEM:** Cellular phone companies often package their products to make them more attractive to potential users. If you average 356 minutes per month in talk time, which package is the better deal.Package A includes a free phone and 300 minutes. It will cost 0.12 per minute for each minute over the plan time. Package A has a base rate of $39.95.Package B has a phone that costs $10 and has 350 minutes of time and 0.08 per minute for each minute over the plan time. Package B has a base rate of $35.95 not including the phone. > The answer should be package B      **2 ADDITIONAL LINKS: http://www.webmath.com/solver.html http://www.sosmath.com/algebra/solve/solve0/solve0.html**
 * The x-value will be the number of minutes–plan time.
 * The b-value will be the base cost of the package plus any charge for the phone
 * The y-value will be the final monthly cost based on 356 minutes