Functions, Relations, and Slope-Intercept Form in Simple English

Published by Mildew
April 15, 2009, Category: Mathematics

Confused about what slope-intercept form is? What about what a relation is? The basics of functions, relations, and slope-intercept form are revealed in this article.

What is Slope-Intercept Form?

Say you’re given a set of numbers in a chart:

X	Y
1	3
2	5
3	7
4	9
5	11

The equation that can be used to determine how this set of ordered pairs are related is “y=2x+1” (This is Slope-Intercept form for this set of ordered pairs)

What this means, is that a number y (a number in the y column) is equal to twice the value of a number x (a number in the x column) plus one. *NOTE* The y and x must be horizontal to each other… i.e. you could use 3&7 but not 3&9

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Look at the “7” in the y column. Directly to the left of it, is a 3. The way these two numbers are related is “y=2x+1”

The x and the y can be plugged in to the equation. By replacing the x in the equation with the appropriate number in the x column (3, in this case) and by doing the same with the y (it should be replaced with 7), your equation will look like:

7=2(3)+1

Simplify, and get:

7=7

You’ve just proven that y=2x+1

Now, here comes the tough part-

How to find slope-intercept form from a set of ordered pairs:

X	Y
1	3
2	5
3	7
4	9
5	11

Looking at the table, pretend you haven’t been told the slope-intercept form for it. How would you determine how these sets of numbers are related?

You find how each section in the y column and each section in the x column change from space to space (going downward):
The y column increases by 2 from space to space. (3+?=5)
Do the same for the x:
The x column increases by 1 from space to space. (1+?=2)
NOW, you use this information to write the slope of the function. You do this by putting the two values that x and y change by into a fraction: change in y over change in x
The x changes by one, while the y changes by two…. 2/1, which equals two— the slope is two!
SO, now we have y=2x. Plug in an x value and a y value, and you’ll realize that it doesn’t come out correctly. Let’s plug in 5 for the y and 2 for the x.
5=2(2)
This is impossible, as 5 is not equal to four
This is because the equation lacks the y-intercept (b)
One way to figure out the y-intercept is to plug in an x and y value to your equation, adding the variable “b”
It should look like this (if you plug in 5 and 2 again): 5=2(2)+b
If you solve for b, you’ll find that b=1
NOW, you’re equation is complete, and looks like this— y=2x+b
By plugging in any number for x you can find the corresponding y value, and vice versa.