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)
 
You may find this equation of a line calculator helpful
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 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

Collinear: When three or more points fall on the same line