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Common Core Standard: 8.EE.C.8
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
How to write linear equations
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
Simple Linear Equations
A linear equation is typically written as y= mx +b
Collinear: When three or more points fall on the same line
Points that lie on the same line can be described as collinear
A
B
C
Collinear
If given two points on a line how do you write the linear equation for the line ?
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
Welcome to MooMooMath. Today we are going to talk about linear equations and checking solutions. So here is our linear equation y = -3x +5. Our slope is negative three and our Y intersect or B is positive five. We are trying to check to see if ( 2,-1) is a solution to this linear equation. In other words “If I drew this line, with a point, would negative one be on that line? “ Well the way to check it is very simple. So let’s look at the rules. All we are going to do is plug in the X value and see if it matches the Y or output value. So let’s try this, let’s plug in our X value and see if we get out the Y. So we are going to plug in the value 2 and see if we get out negative 1. OK let’s plug in X so negative three times two plus five. We are trying to check “are we going to get out a negative one? “ Let’s see negative three times positive two is six. Negative six plus five equals -1. “Do we get a negative one?” Yes we do, so guess what? This point two, negative one is a solution. That just means that two, negative one falls on that line. Hope this was helpful.