# Write an equation that shows the relationship between quantities

### Writing proportional equations from tables (video) | Khan Academy

Writing an equation to describe the relationship between the number of the video shows the. The student cannot write a correct equation because he or she does not Explain to the student how the equation shows the relationship between the variables. But it's just as important to know how to write equations and expressions. Once this to find out. The quantities that we already know are written in an expression as numbers. The relationships among variables and constants are described by mathematical symbols that show operations to be carried out, such a + and −.

**How to Determine if a Relationship Represented in a Table Is Linear & Write an Equation : Algebra**

Which variable is independent? Which variable is dependent?

How is the dependent variable related mathematically to the independent variable? Instructional Implications Ask the student to identify the independent and dependent variables and to verbally describe the relationship between them. Guide the student to describe precisely, in mathematical terms, how to calculate a value of the dependent variable from a value of the independent variable. Then assist the student in mathematically representing this relationship with an equation.

Provide additional problem contexts that can be modeled by an equation in two variables. Encourage the student to analyze the relationship using a table or graph and then write an equation that reflects the relationship between the variables. The student provides no explanation. Questions Eliciting Thinking Which variable is independent dependent?

How are the independent and dependent variables related in the table?

## Writing proportional equations from tables

What is the meaning of each change in the independent variable? What does it mean when n increases by one?

What happens to g when n increases by one? How come you have to subtract three from the number of sides? What happens to d each time s changes?

Instructional Implications Review the terms dependent variable and independent variable. Clarify that both the dependent and independent variables change, though in different ways. Change in the dependent variable depends on change in the independent variable. Explain that typically the value of the independent variable is freely chosen, but the value of the dependent variable is calculated for particular values of the independent variable.

It might be helpful to describe these variables in terms of an input-output system where the independent variable is the input and the dependent variable is the output. Upon questioning, the student can identify the constant of proportionality, 18 inches, and understands that the solution to the equation is three handle turns. However, the student does not know how to write an equation having two variables. The student can identify the constant of proportionality, 18 inches, but cannot write an equation having two variables.

What does the variable stand for in your equation? What does the 18 represent in your equation? Can you solve your equation? What does the solution to your equation represent? Can you write an equation using two variables?

### Relationships between quantities in equations and graphs (practice) | Khan Academy

What do you think the other variable could stand for? What is the constant of proportionality? Instructional Implications Provide instruction on writing equations with two variables to represent proportional relationships. Compare an equation having one variable with an equation having two variables. Point out how the former represents the relationship between a specific number of handle turns and the total inches of line retrieved; whereas, the latter represents the constant relationship between the two variables.

Provide additional opportunities for the student to practice writing equations to represent proportionally related values displayed in a graph. Examples of Student Work at this Level The student writes a correct equation e. Instructions for Implementing the Task This task can be implemented individually, with small groups, or with the whole class.

- Writing An Equation
- Analyzing the Relationship
- Table to Equation

The teacher asks the student to complete the problems on the Analyzing the Relationship worksheet. The teacher asks follow-up questions, as needed. Consequently, the student is unable to correctly describe the relationship between the independent and dependent variables. Questions Eliciting Thinking How did you calculate the values for T in the chart? Did you use the equation? What does the variable T represent?

What does the variable w represent? Guide the student to select reasonable values of w such as 0, 1, 2, 3, and 4 and make explicit that these values represent numbers of weeks. Model calculating a value of T and remind the student to apply the order of operations rules when evaluating expressions. Ask the student to calculate the remaining values of T.

### Writing proportional equations (practice) | Khan Academy

Guide the student to relate each value of T to its associated value of w. Model explaining the meaning of a coordinate pair [e. Point out that the value of T depends on the value of w. Review the terms dependent and independent if needed.

Clarify that because both are variables, they both can change. Change in the dependent variable depends on the change in the independent variable.

It may be helpful to use the terms input and output.