Linear Equations and Properties

This video tutorial covers the identification of linear and nonlinear functions, focusing on the slope-intercept form of linear equations. It explains how to determine if a function is linear or nonlinear by analyzing the equation and graph. The tutorial also discusses the concept of proportionality in linear relationships and demonstrates how to rearrange equations to identify linearity. The video concludes with guidance for further learning and additional resources.

What is the standard form of a linear equation?

• Y = mx + b

• Y = x^2

• Y = ax^2 + bx + c

• Y = a/x

What does the equation Y = x^2 represent in terms of a square tile?

• The perimeter of the tile

• The area of the tile

• The diagonal of the tile

• The volume of the tile

What shape does the graph of Y = x^2 form?

• A triangle

• A curve

• A circle

• A straight line

Why is the relationship between X and Y in Y = x^2 considered nonlinear?

• The graph forms a straight line

• The slope is constant

• The slope is not constant

• The equation can be written in slope-intercept form

What is the slope of the line if the change in Y is 4 and the change in X is 1?

• 3

• 2

• 1

• 4

How can you rearrange the equation Y = 8 + x to determine if it is linear?

• Y = 8x

• Y = x + 8

• Y = x^2 + 8

• Y = 8/x

What does the commutative property of addition allow you to do?

• Multiply numbers in any order

• Add numbers in any order

• Subtract numbers in any order

• Divide numbers in any order

What is the coefficient of X in the equation Y = -1x + 5?

• 0

• 5

• 1

• -1

Which of the following equations is linear?

• Y = x^3

• Y = 1/x

• Y = x^2 + 3

• Y = 2x + 5

What does a negative sign to the left of a variable indicate?

• The variable is positive

• The variable is negative

• The variable is undefined

• The variable is zero