Which of the following is not a linear equation?
In the world of mathematics, linear equations play a crucial role in representing straight lines on a two-dimensional plane. They are fundamental to various fields, including algebra, calculus, and physics. However, not all equations can be classified as linear. This article aims to identify the equation that does not fit the linear category among the given options.
The linear equation is typically represented in the form of y = mx + b, where ‘m’ is the slope of the line, and ‘b’ is the y-intercept. This form is also known as the slope-intercept form. Linear equations are characterized by their constant rate of change, which means that the slope remains the same throughout the entire line.
Let’s examine the following options to determine which one is not a linear equation:
1. y = 2x + 3
2. y = 3x^2 + 4
3. y = -5x + 1
4. y = 4x – 6
Option 1, y = 2x + 3, is a linear equation because it follows the slope-intercept form. The slope (m) is 2, and the y-intercept (b) is 3.
Option 2, y = 3x^2 + 4, is not a linear equation. It is a quadratic equation because it contains the variable ‘x’ raised to the power of 2. The presence of the squared term indicates that the rate of change is not constant, making it a non-linear equation.
Option 3, y = -5x + 1, is a linear equation as it adheres to the slope-intercept form. The slope (m) is -5, and the y-intercept (b) is 1.
Option 4, y = 4x – 6, is also a linear equation. It has a slope (m) of 4 and a y-intercept (b) of -6.
In conclusion, among the given options, y = 3x^2 + 4 is not a linear equation. It is essential to recognize the characteristics of linear equations and differentiate them from other types of equations to better understand their applications in various fields.
