Expressing Variables in Equations

This lesson focuses on writing equations based on tables, exploring the relationship between dependent and independent variables. It provides examples of expressing Y in terms of X and vice versa, using tables to identify patterns and derive equations. The lesson also covers fractional and decimal equations, emphasizing the importance of understanding how to manipulate equations to express variables in different forms. The session concludes with a summary and a preview of the next lesson.

What is the dependent variable in an equation where y is expressed in terms of x?

• Neither x nor y

• Both x and y

• y

• x

Which of the following is an example of y being expressed in terms of x?

• x = 3y + 1

• x = y - 5

• y = x + 2

• y = 2x - 3

If a table shows that y is always three times x, what is the equation?

• y = x - 3

• y = 3x

• y = x/3

• y = x + 3

In a table where y is always 2 less than x, what equation represents this relationship?

• y = x/2

• y = 2x

• y = x - 2

• y = x + 2

How can you express y as half of x using a decimal?

• y = x/2

• y = 2x

• y = 0.5x

• y = x + 0.5

What is the equation if y is one-fourth of x?

• y = 0.25x

• y = x/4

• y = 4x

• y = x + 4

If y is expressed as 25 hundredths of x, what is another way to write this equation?

• y = 4x

• y = x + 0.25

• y = 0.25x

• y = x/4

How can you express x in terms of y if x is four times greater than y?

• x = y/4

• x = 4y

• x = y - 4

• x = y + 4

What happens to the equation when you switch from y in terms of x to x in terms of y?

• The equation becomes negative

• The equation uses a whole number

• The equation becomes a fraction

• The equation remains the same

In the context of the lesson, what does it mean to 'flip' an equation?

• To multiply both sides by 2

• To express x in terms of y

• To add a constant to both sides

• To change the sign of the equation