Which of the following is a linear equation?

Which of the following is a linear equation?

• A. y = 3x + 2
• B. y = x^2 + 1
• C. y = \frac{1}{x}
• D. y = 2x^3 - 3

Answer: (A)

A linear equation is defined as an equation of the first degree, which means it has a degree of one. This type of equation represents a straight line when graphed in a coordinate plane. The general form of a linear equation in two variables (x and y) is expressed as \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept. In the given equation \(y = 3x + 2\), it fits the linear equation format perfectly: \(3\) is the coefficient of \(x\), making the slope \(m = 3\), and \(2\) is the constant term, which indicates the y-intercept at the point \((0, 2)\). Therefore, this equation will graph as a straight line. In contrast, the other options represent equations of higher degrees or non-linear relationships. The equation \(y = x^2 + 1\) is quadratic, showing a parabolic curve rather than a straight line. The equation \(y = \frac{1}{x}\) is a rational function that has hyperbolic characteristics, resulting in a curve that approaches the axes but never touches them. Lastly, the equation

A linear equation is defined as an equation of the first degree, which means it has a degree of one. This type of equation represents a straight line when graphed in a coordinate plane. The general form of a linear equation in two variables (x and y) is expressed as (y = mx + b), where (m) represents the slope and (b) represents the y-intercept.

In the given equation (y = 3x + 2), it fits the linear equation format perfectly: (3) is the coefficient of (x), making the slope (m = 3), and (2) is the constant term, which indicates the y-intercept at the point ((0, 2)). Therefore, this equation will graph as a straight line.

In contrast, the other options represent equations of higher degrees or non-linear relationships. The equation (y = x^2 + 1) is quadratic, showing a parabolic curve rather than a straight line. The equation (y = \frac{1}{x}) is a rational function that has hyperbolic characteristics, resulting in a curve that approaches the axes but never touches them. Lastly, the equation