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Slope Intercept and Linear Equations

Any straight (linear) line can be shown by using one frequently used equation. The formula is a linear equation, meaning it produces a single, straight line. This equation is:

Y = mx + b

The slope of the line is represented by m which is:

m = change in Y / change in X

This is also commonly called the "rise over run," meaning the amount the line rises over the amount the line "runs" left to right.

b = where the line crosses the Y axis.

A fully completed equation looks like: Y = 2x + 3, and is graphed below:

How to graph the linear equation
Graphic the equations is fairly easy. First, start with your "b" value. We'll use Y = 2x + 3 as an example. The "b" value is 3. Find this position on the graphic, and put a dot there.

Next, since the slope (2x) is positive, the line will be going higher and higher (from left to right.) If it were negative, the line would be going lower and lower. Since 2 is the same as 2/1, we can go up to our b=3 dot, and see that in our "rise/run" equation, the rise is 2. So, simply go up 2 values. The "run" is equal to 1, so go to the right 1 value and draw another dot. Continue going up 2 values and over 1 value until you have enough to draw a straight line (usually 3 dots is enough.) That's all there is to it!

How to create a linear equation from two points
If you know as little 2 points in a line, you can easy determine the entire equation. Let's see how this would work.

1. Find the equation of the line whose points include (-5, 2) and (4, -1) and crosses the Y axis at 2.

To find the slope, we use this equation:

m = (y2 - y1) / (x2 - x1)

This makes our equation:

m = (-1 - 2) / (4 - -5) = -3 / 9 = -1/3

And we have: Y = -1/3X + 2.

Here is another to try:

2. Find the equation of the line whose points include (4, 2) and (1, 3) and crosses the Y axis at 3.

Step 1: m = (3 - 2) / ( 1 - 4) = 1 / -3

And we have Y = -1/3X + 3!

Pretty simple once you get the hang of it!

 

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