Linear Equations and Characteristics

The video tutorial explains how to determine if an equation is linear. It introduces the standard form of linear equations, y = mx + b, and outlines two key rules: no variables in the denominator and no variables multiplied by each other. Through examples, the tutorial demonstrates how to identify linear and non-linear equations based on these rules.

What is the standard form of a linear equation?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b/x

Which of the following is NOT allowed in a linear equation?

• A variable in the denominator

• A variable added to another variable

• A constant term

• A variable with a coefficient

Which of the following is a characteristic of a linear equation?

• Quadratic terms

• Variables in the denominator

• No variables multiplied by each other

• Exponential terms

In the equation y = 1/5x + 12/5, what is the value of m?

• 5

• 12/5

• 1

• 1/5

How can you rewrite the expression x/5 + 12/5?

• y = 5/x + 12

• y = x + 5/12

• y = 5x + 12

• y = 1/5x + 12/5

What is the y-intercept (b) in the equation y = 1/5x + 12/5?

• 1

• 5

• 1/5

• 12/5

Which of the following is a valid linear equation?

• y = 3x^2 - 4

• y = 7/x - x/x

• y = x^2 + 2x + 1

• y = 1/5x + 12/5

Why is the equation y = 7/x - x/x not linear?

• It has no variables

• It is already in the form y = mx + b

• It has a constant term

• It has a variable in the denominator

What happens to the x terms in the equation y = 7/x - x/x?

• They add up to give zero

• They cancel out to give one

• They remain unchanged

• They multiply to give x^2

What is the main reason y = 7/x - x/x is not linear?

• No variables

• Squared term

• Constant term

• Variable in the denominator