# Simple Linear Equations

## Common Core Standard: 8.EE.C.8

If given two points on a line how do you write the linear equation for the line?

## A linear equation is typically written as y= mx +b

*m = slope*

*b=y intercept***When asked to write an equation you are simply writing an equation to match a graph.**

An example question that involves writing an equation is:

Find the equation of a line that passes through the given points.

## Quick Overview

- Find slope

- Plug slope into y=mx+b (y intercept form)

- Plug in x or y to find b (y intercept)

- Write the equation

Find the equation for a line that passes through the two points:

(3,1) and (7,4)

**Step 1**. Find the slope using the slope formula

Slope =3/4

**Step 2.**Plug the slope into the slope intercept formula

y=3/4x + b

**Step 3.**Plug in either of your given (x,y) values and solve for b

1 = ¾*3 + b

b = -5/4

**Step 4.**Write the equation

**y = 3/4x – 5/4**

Video provides step by step directions for solving:

*Find the equation for a line that passes through the two points:*

*(3,1) and (7,4)***Given a linear equation how do you know if points fall on the line created by the linear equation?**

Do the coordinates (2,-1 ) fall on the line created by the linear equation y = -3x + 5 ?

Follow these steps in order to see if (2,-1) falls on the line.

1. Plug in the value for X into the equation.

2. Check to see if it matches the given

**Y**value.3. If the answer matches the Y value then both points fall on the line.

*Example 1*Given the linear equation y=-3x + 5

do the cordinates (2,-1) fall on the line of the linear equation?

**Step 1**.y = -3*2 +5 plug the x value into the equation

**Step 2**y =-6 +5

**Step3**y =-1

So the cordinates (2,-1) fall on the line of the linear equation y=-3x +5

*Example 2*Given the linear equation y = 2x +6

do the cordinates (3,-2) fall on the line of the linear equation?

**Step 1**. y=2*3 +6 plug the x value into the linear equation

**Step 2**. y = 6 +6

**Step 3**. y = 12

The cordinates (3,-2) do not fall on the line of y=2x+6 because the value for y does not equal -2

*Points that lie on the same line can be described as collinear*