# Define Linear Equation

**Common Core Example: 8.EE.C.8**

A **linear equation **is an equation that describes a straight line. One form of a linear equation is the **slope intercept form** which is written,** y=mx +b.** In this equation the **m** represents the **slope **of the line and the **b** represents the** y intercept.**

For example,** y= 4x + 3** means: the line has a **slope of +4**, and crosses the** y intercept at 3**. There are several forms of linear equations including, **slope intercept form, point slope formula**, and the **standard form**. A different forms allow you to describe the same line in different ways.

m=

**the slope**, which is calculated by counting**Rise over Run.**

**Slope can also be calculated using the slope formula, when you have two points on the line:**

b=

**the y-intercept.**This is the point in which the line intercepts the y-axis.## Writing linear equations

**Given a graph:**

1. Find the slope by counting rise or run

2. Identify the y intercept (where the line crosses the y-axis)

3. Plug in slope which is represented by m, and the y-intercept represented by b, into the formula

**y =****m****x +****b**## Different types of linear equations

**Slope-intercept form: y=mx+b**

-use when you have a graph or

-when you have the slope and y-intercept

**Point-slope form: y-y**

**1**

**= m(x-x**

**1**

**)**

-use when you know the slope and one point

x1 and y1 are known points

m =slope

x and y are any other points on the line

**Standard Form**

Ax +By =C

A,B,C, are all numbers

Use when you want to graph. Use when you want know the x intercept.

For example y=2x-2

Rewrite 2x-y=2

A = 2

B= -1

C =2

**Written as a function:**

A line can be written in function notation by replacing y with f(x).

f(x) = mx +b

**Identity function: f(x) =x**

An identity function is used when your input equals your output.

Ex. (1, 1), (-3, -3) or (100, 100)

This parent graph is a line with a slope of 1 and a y-intercept of 0.