A linear equation is an algebraic expression that consists of two variables (usually represented by x and y) and an equals sign, with the goal of finding the value of the variables that make the equation true. It has a constant rate of change and forms a straight line when graphed.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants and x and y are variables. This form allows for easy identification of the slope and y-intercept of the line.
To graph a linear equation, you can use the slope-intercept form (y = mx + b) or the standard form (Ax + By = C). Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to find additional points on the line. Finally, connect the points with a straight line.
A linear equation is an algebraic expression, while a linear function is a mathematical relation between two variables (x and y) that can be represented by a line. A linear function is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.
Linear equations have many real-life applications, such as calculating the growth or decline of a population, determining the cost of a phone plan based on minutes used, or predicting the distance a car can travel based on its speed. They are also used in fields like economics, engineering, and physics to model and solve problems.