Hello, and welcome to this video on linear equations!
In this video we will look at what linear equations are,
and how to solve for different variables in a linear equation.
What exactly is a linear equation?
Well, if you look at the word ‘linear’ you can find the word ‘line’, so a linear equation is an equation for a line.
Linear equations have two variables, most commonly x and y, that are to a single degree,
meaning they do not have variables to powers or roots.
Y equals 9x plus 5 is an example of a linear equation.
Let’s look at some equations and determine if they are linear.
As each question is written on the board, I want you to decide if it is linear or not.
Y = x squared plus 2.
No, this is not a linear equation because the x variable is squared.
Y equals 4x plus 1
Yes, this is a linear equation.
There are two variables and they are both of a single degree.
X plus 3y equals 7
Yes, even though this equation looks a little different from our other ones,
it is still a linear equation because there are two variables,
and neither one has a root or is raised to a power.
X equals the square root of y minus 4
No, this is not a linear equation because of the square root.
The most common way you will see linear equations is in the form “y equals”.
Because this is the easiest way to create a graph based on the equation.
This is called slope-intercept form.
However, it is still okay to have an equation with the x variable, or both the x and the y variables,
on the left side of the equation.
Let’s look at an equation that has the x variable on the left side and rearrange it so it is in slope-intercept form.
X equals 2y minus 7
When we are looking for slope-intercept form,
we want to get the y variable by itself on the left side of the equation.
To do this, we first have to add 7 to both sides.
X plus 7 equals 2y
Then we divide by 2 to get y by itself.
Remember, dividing by 2 is the same as multiplying by one half, so another way to write this equation is:
one half X plus seven halves equals Y
All that’s left is to flip our equation around so the y is on the left side of the equation.
Y equals one half X plus seven halves.
Now we have our equation in slope-intercept form!
Let’s look at one more equation, but this time we are going to solve for x.
6y minus 3x equals 12
Our first step to get our x variable by itself on the left side is to subtract 6y from both sides of the equation.
So we have negative 3x equals 12 minus 6y
Then, we divide the whole equation, which means both parts of the right-hand side of the equation,
by negative 3.
So X equals negative 4 plus 2y
This is technically correct,
but the best way to write an equation like this is to have the variable before the number,
so we are going to rearrange it to look like this.
X equals 2y minus 4
Remember, the other way wasn’t incorrect, but this is the more proper way to write our equation.
I hope this overview of linear equations was helpful!
Thanks for watching and happy studying!