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Common Core Example: 8.EE.C.8
Standard Form
Ax +By =C
A,B,C, are all numbers
Use when you want to graph. Use when you want know the x intercept.
For example y=2x-2
Rewrite 2x-y=2
A = 2
B= -1
C =2
Equation of a Line
Define Linear Equation
m= the slope, which is calculated by counting Rise over Run.
Slope can also be calculated using the slope formula, when you have two points on the line:
b= the y-intercept. This is the point in which the line intercepts the y-axis.
In this example the slope or m = 2/3
The y-intercept or b = -2
Resulting in the equation
- y= 2/3x - 2
Y intercept
A linear equation is an equation that describes a straight line. One form of a linear equation is the slope intercept form which is written, y=mx +b. In this equation the m represents the slope of the line and the b represents the y intercept. For example, y= 4x + 3 means: the line has a slope of +4, and crosses the y intercept at 3. There are several forms of linear equations including, slope intercept form, point slope formula, and the standard form. A different forms allow you to describe the same line in different ways.
Remember the X axis runs horizontally and the Y axis runs up and down or vertically.
Rise 2
Run 3
For additional help with Linear Equations visit Slope of a Line
The formula for a linear equation is y= mx +b
Slope
y intercept
Writing linear equations
Given a graph:
1. Find the slope by counting rise or run
2. Identify the y intercept (where the line crosses the y-axis)
3. Plug in slope which is represented by m, and the y-intercept represented by b, into the formula y = mx + b
Different types of linear equations
Slope-intercept form: y=mx+b
-use when you have a graph or
-when you have the slope and y-intercept
Point-slope form: y-y1 = m(x-x1)
-use when you know the slope and one point
x1 and y1 are known points
m =slope
x and y are any other points on the line
Written as a function:
A line can be written in function notation by replacing y with f(x).
f(x) = mx +b
Identity function: f(x) =x
An identity function is used when your input equals your output.
Ex. (1, 1), (-3, -3) or (100, 100)
This parent graph is a line with a slope of 1 and a y-intercept of 0.
Hi Welcome to MooMooMath. Today we are going to look at the basic equation of a line. We usually try to write the line in what is called y intercept form which is y equals mx plus b. The x and y are variables and the M stands for slope and we can remember this by M stands for mountains and mountains have slope and then b is your y intercept. So here is a line graph and the other thing you have to notice is that in a linear equation X is always to the first power. We don’t write it, we assume that there is a little 1 here so any time we have an X to the first power we know we have a linear equation. So next we are going to count our slope and this one has a 3 over 3 slopes (rise3, run 3) so that means we have a slope of 1. Now let’s look at another example and here is our Cartesian coordinate plane and we will draw a line. So I will write the equation Y=mx +b. Next I will underline all that I need to replace. I need to find m and I will need to find b so let’s count our slope. It looks like it goes up 2 and over 3 so my slope is 2/3 X. Now I need to find the intercept. Where does the line cross the Y axis? It goes up two but it is below the X axis so it is negative 2. So my final equation will be y= 2/3x -2 Here is a quick overview. The equation is y=mx + b m=the slope, b=the y intercept and x and y are variables. You take Y= ___ X = ____ and fill in m for the slope and y for the b intercept. So looking at this example the slope is 2 over 1 or 2 and the line intercepts at 2 so the equation will be Y = 2x + 2 Hope this video was helpful.