# CLASS-6LINEAR EQUATIONS

LINEAR EQUATION -

A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It is characterized by variables raised to the power of 1 and does not contain any higher power of the variables. A general linear equation can be written in the form:

ax + by = c

Where:-

• x and y are variables.
• a, b, and c are constants, with a and b not being equal to zero simultaneously.

Linear equations can take different forms, and they can involve more variables, but the most basic form involves two variables (x and y) as shown above.

The goal in working with linear equations is often to find the values of x and y that satisfy the equation, which corresponds to finding the point where the line represented by the equation intersects the coordinate plane.

Here are some key terms and concepts related to linear equations:-

1. Slope-Intercept Form:-

A commonly used form of a linear equation is the slope-intercept form:

y = mx + b

Where:-

• m is the slope of the line, which represents the rate of change of y concerning x.
• b is the y-intercept, which is the point where the line crosses the y-axis (when x = 0).

2. Point-Slope Form:-

Another form of a linear equation is the point-slope form:

y − y₁ = m (x − x₁)

Where:-

• m is the slope of the line.
• (x₁, y₁) is a point on the line.

1. Standard Form:-

The standard form of a linear equation is the one mentioned earlier, ax + by = c, where a, b, and c are constants, and both a and b are not zero.

2. Solution of a Linear Equation:-

The solution to a linear equation is the pair of values (x, y) that makes the equation true. In other words, it is the point on the graph where the line intersects the coordinate plane.

2. Graph of a Linear Equation:-

When graphed on a coordinate plane, a linear equation represents a straight line. The slope of the line determines its steepness, and the y-intercept determines where it crosses the y-axis.

3. System of Linear Equations:-

A system of linear equations consists of multiple linear equations with the same variables. The solution to a system is the set of values for the variables that satisfy all the equations simultaneously.

Linear equations are fundamental in mathematics and have numerous applications in science, engineering, economics, and many other fields. They are relatively simple to solve and analyze, making them an important building block for more complex mathematical and scientific problems.