Linear Functions and Their Characteristics

This video tutorial explains how to identify linear and non-linear graphs and equations. It begins by introducing the concept of linear functions, which create straight lines, and non-linear functions, which do not. Examples of both types of functions are provided. The video then delves into linear equations, explaining common forms such as y = mx + b and ax + by = c. Key properties of linear equations are discussed, including the requirement that the largest exponent must be one, and x and y must be in separate terms and in the numerator. The tutorial concludes with practical examples of identifying linear and non-linear graphs and equations.

What is a key feature of a linear function?

• It forms a curve.

• It forms a straight line.

• It forms a zigzag pattern.

• It forms a circle.

Which of the following is a non-linear function?

• y = 5x + 7

• y = 2x + 3

• y = x^2 + 1

• y = 3x - 4

What is the standard form of a linear equation?

• ax + by = c

• y = x^2 + bx + c

• y = mx + b

• y = ax^2 + bx + c

Which of the following equations is in slope-intercept form?

• xy = 5

• x^2 + y = 4

• 2x + 3y = 6

• y = 3x + 2

In a linear equation, what must be true about the exponents of x and y?

• They must be two.

• They must be one.

• They must be negative.

• They must be zero.

Why can't x and y be multiplied together in a linear equation?

• It would make the equation quadratic.

• It would make the equation non-linear.

• It would make the equation cubic.

• It would make the equation exponential.

What happens if a variable is in the denominator of a linear equation?

• The equation remains linear.

• The equation becomes non-linear.

• The equation becomes quadratic.

• The equation becomes undefined.

Which of the following is NOT a characteristic of a linear equation?

• Exponents are one.

• Variables are multiplied together.

• Variables are in the numerator.

• Terms are separated by addition or subtraction.

Which graph represents a linear function?

• A parabola

• A straight line

• A cubic curve

• A circle

What is the form of the equation y = 5x - 7?

• Slope-intercept form

• Standard form

• Exponential form

• Quadratic form