A linear equation is an equation that contains two variables, usually represented by x and y, and can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. Linear equations form a straight line when graphed and have a constant rate of change.
An equation is linear if it can be written in the form of y = mx + b, where m and b are constants. This means that the variables x and y are not raised to any power and are only multiplied by constants. Additionally, when graphed, linear equations form a straight line.
The term "linear" refers to the fact that the equation represents a straight line when graphed. This is due to the constant rate of change between the two variables in the equation.
Yes, x1+x2=x3+x4 is a linear equation. It can be rewritten as x1-x3=x4-x2, which follows the form of y = mx + b, where m = -1 and b = 0. This means that when graphed, the equation will form a straight line with a slope of -1 and a y-intercept of 0.
Linear equations are fundamental to many fields of science, including physics, engineering, and economics. They provide a way to model and analyze relationships between variables and make predictions based on data. Understanding linear equations also lays the foundation for more complex mathematical concepts and problem-solving skills.