# Two Variable Equations Worksheets

In this section you will be given a premade function table that you will need to evaluate and write an equation for to model what is happening over the course of the system. You are basically mathematically modeling an input and output situation. This is one of those skills that have a high level of crossover to the real world. When we look at equations or situations where we have to make sense of what is going on with a system, it teaches us how to spot situations that we can make better from. It also shows us how small subtle changes can have a significant impact on mathematical equation or expression. This collection of worksheets and lessons that help students write their own equations with multiple variables.

### Aligned Standard: HSA-CED.A.2

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - What's the rule that you can determine from the inputs and the resulting outputs.
- Quiz 2 - Is it A or B? You are given a table and then asked which function will apply.
- Quiz 3 - Tom walks 5 km in 3 hours. Write an equation that shows the relationship between the time h and the distance d Tom ran?

### Writing Equations that Describe Function Tables

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 and y = -2, 1, 4, 7.

The equation of a line is presented in this form: y = mx + b. Where m= slope and b = 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.

You can also apply this technique to solve many different real-world situations. When you look at the linear equation remind yourself that in any situation where there is constant rate of change you can manipulate it to determine future growth or decay.