## Creating Equations with Two or More Variables

#### Aligned To Common Core Standard:

**High School** - HSA-CED.A.2

How to Write an Equation that Describes a Data Table?
A data table usually consists of values of x and y values. It is easy to find and write the equation when you have a table consisting of x and y values.
Consider a table with the following values;
X = 0, 1, 2, 3
y = -2, 1, 4, 7
We know from previous lines that the equation for linear data is given by;
y = mx + c
Here, m= Slope, c= y-intercept
The y-intercept is where the line cuts the y-axis and at this point x=0, here the y-intercept is -2. In case the data is not so straightforward, you will have to calculate the y-intercept after you know the slope.
There are two methods of determining the slope using a data table.
**Using formula ** -
We know that in coordinate geometry, the slope is given by the formula;
m=(y_{1}- y _{2})/(x_{2} - x_{1})
Take any two points from the data table, substitute it in this formula, and you get the slope.
**Common Difference** -
The second method to calculate slope is to find the common difference between the x values and the y values. It is a straightforward method to determine slope as it is given by change in y divided by change in x.
If you closely analyze the data table, you see that y increases with a common difference of 1 and the values of y increase by 3.
Using any of these techniques, we find out that the slope is; m=3
Now that you know the slope and the y-intercept you can easily write the equation as; y=3x - 2. This collection of worksheets and lessons that help students write their own equations with multiple variables.

### Printable Worksheets And Lessons

- Equation As Inputs
Step-by-step Lesson- Determine which equation gives you the
output displayed in the table.

- Guided Lesson
- The first two problems are simple plug and chug. The word problem
is a bit more challenging. Don't get lost in the words.

- Guided Lesson Explanation
- The first two require you to write a linear equation. The last
one makes you create your own table to start with.

- Practice Worksheet
- When you complete this sheet, you should really have a handle
on this skill.

- Matching Worksheet
- This is one of the toughest sheets to create thus far for this
site.

#### Homework Sheets

The first two look for the rule for the given tables. The last sheet is in word problem form.

- Homework 1 - Linear functions are of the form y = mx + b First find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 1. This means that m is equal to 1.
- Homework 2 - Find the equation that gives the rule for this table?
- Homework 3 - Jo made 3 home made chocolates in a day. Write an equation that shows relationship between the days d and the number of chocolates c Jo made.

#### Practice Worksheets

I followed the same pattern here are I did on the homework.

- Practice 1 - Which equation gives the rule for this table?
- Practice 2 - Find the equation that gives the rule for this table?
- Practice 3 - Mark starts a car wash. He washes 10 cars in a day. Write an equation that shows the relationship between the number of days d and the number of cars Mark washes c?

#### Math Skill Quizzes

Once again, the first two are rule based problems and the last is in sentence form.