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=(y1- y 2)/(x2 - x1) 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
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.
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.