Identifying Linear and Nonlinear Graphs and Equations

The video tutorial explains how to identify linear and non-linear graphs and equations. It begins by discussing the characteristics of linear functions, which form straight lines, and contrasts them with non-linear functions, which do not. The tutorial then delves into linear equations, highlighting 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 1, x and y must be in separate terms, and both must be in the numerator. The video concludes with practical examples of identifying linear and non-linear graphs and equations.

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

• It forms a circle.

• It has two curves.

• It creates a straight line.

• It forms a V shape.

What is the standard form of a linear equation?

• y = mx + b

• ax + by = c

• x^2 + y^2 = r^2

• y = ax^2 + bx + c

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

• They can be any positive number.

• They must be 2.

• They must be 0.

• They must be 1.

Why can't a linear equation have a variable in the denominator?

• Because it would make the equation cubic.

• Because it would make the equation quadratic.

• Because it would result in a negative exponent.

• Because it would make the equation circular.

Which of the following equations is non-linear?

• y = 5x - 7

• 2/5x - y = 0

• y = 3x/4 + 1

• x * y = 4