Linear Equations and Their Properties

The video tutorial explains how to determine if an equation is linear or non-linear by rearranging it into the form y = mx + b. It provides multiple examples, demonstrating the process of isolating y and checking the equation's format. The tutorial emphasizes the importance of recognizing the presence of x squared terms, which indicate non-linearity. The video concludes with tips for identifying linear equations using algebraic manipulation.

What is the standard form of a linear equation?

• y = a/x + b

• y = ax + b

• y = ax^2 + bx + c

• y = mx + b

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

• Contains x^2

• Can be rearranged to y = mx + b

• Has a variable in the denominator

• Includes a square root

What is the first step in converting 8x + 2y = 36 to y = mx + b format?

• Multiply by 2

• Divide by 2

• Add 8x to both sides

• Subtract 8x from both sides

After isolating y in 8x + 2y = 36, what is the coefficient of x?

• -4

• 4

• -8

• 8

Why is x^2 + y = 11 considered non-linear?

• It has a constant term

• It contains x^2

• It can be rearranged to y = mx + b

• It has no x term

What operation is performed to isolate y in x^2 + y = 11?

• Subtract x^2 from both sides

• Multiply by x

• Divide by x

• Add x^2 to both sides

In the equation 7x - 5y = 20, what is the result of dividing both sides by -5?

• y = -7/5x + 4

• y = 7/5x - 4

• y = 7/5x + 4

• y = -7/5x - 4

What is the slope of the line represented by 7x - 5y = 20?

• -7/5

• 5/7

• 7/5

• -5/7

How do you isolate y in the equation y/x = 2?

• Subtract x from both sides

• Add x to both sides

• Divide both sides by x

• Multiply both sides by x

What is the y-intercept of the equation y = 2x?

• 1

• 0

• 2

• -2