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