Chapter 2.2

Linear Equations

WARM UP!

3

2

-1

1

3

5

7

Is this a function?

Find w(-2) if w(x) = 3w + 8

By the end of this lesson you will be able to:

Know what a linear equation is

Know what a linear function is

Put a linear equation in standard form

Graph a line using the x and y intercepts

Linear Equations:

An equation such as x + y = 4 is called a linear equation

They have no operations other than addition, subtraction, and multiplication of a variable by a constant.

Linear Equations Continued:

The variables may not be multiplied together or appear in a denominator.

A linear equation does not contain

variables with exponents other than one.

Examples:

Linear Equations: Not Linear Equations:

5x – 3y = 7 7a + 4b2 = -8

Y = ¾x x + xy = 1

X = 9 y = 5x

Linear Functions:

A Linear Function that can be written as Y=mx +b where m and b are real numbers

For example:F(x) = 10 – 5x (yes)F(x) = x4 -5 (no)F(x) = 2xy (no)

Standard Form:

The standard form of a linear equation is Ax + By = C

A and B must be whole numbers A must be positiveSo… manipulate the equation so that

both x and y are on the same side of the equal sign and that the coefficients are not decimals or fractions.

Finding X and Y Intercepts:

3x + 2y = 8To find the X-intercept – set the y variable

equal to zero

To find the Y-intercept – set the x variable equal to zero

Graphing Using the X and Y Intercepts:Once you find both intercepts, plot them

on the same coordinate plane.Connect the points with a line.This is the graph of the equation.

Tonight’s Homework:

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