Linear models for "Codependent" Variables
	Ideas	"Standard form" Ax + By = C Converting between forms (standard and slope-intercept)
	Objective	When finished with this section, the student will be able to graph a linear equation that is in standard form. When finished with this section, the student will be translate between standard and slope-intercept forms of equations.

So far in this unit we have focused on the "slope-intercept" form for a line: y = m·x + b.
Those equations presume that one variable depends on another—which is the case most of the time.

Sometimes variables depend on each other. That is, sometimes there is not a true "independent" or "dependent" variable. Let's call those "codependent" variables.
You will be investigating such situations in this lesson.

The form we often use for "codependent" variables is called "standard form".

A line's equation is in standard form if it is written as Ax + By = C, where the points on the line are (x, y) ordered pairs and the variables A, B, and C are integers.

An example of a linear equation in standard form. Do you see that what happens to the equation if you take the coordinates of any point on that line and substitute them into x and y in the equation? Try the point (8, -3) for example.

Do you notice that the slope of that line in the blue box above is "down 3 over 4" or − ¾ ?
Since the vertical intercept of that line is 3, the equation 3x + 4y = 12 must be the same as y = − ¾ x + 3.
You will have a chance to practice using your algebra skills to "solve for y" in this lesson.

Here's one example for you.

Example: Rewrite the equation 3x + 4y = 12 into "slope-intercept" form for a line ( y = m·x + b).

Solution: 3x + 4y = 12 Given 4y = −3x + 12 Subtracted 3x from both sides Divided both sides by 4. Dividing 4 into each part of the numerator Simplifying

 

 

For your first assignment in this lesson you will look at how two sharks are thinking about ordering sandwiches.
Get your thinker in high gear to really understand "codependent" variables.

Click here to download Assignment 7.04a

This second assignment in this lesson has many basic practice problems.

Click here to download Assignment 7.04b