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A linear equation is one in which the greatest power of the variable is always 1. Another term for it is a one-degree equation. A linear equation with one variable is expressed as Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is a constant. A two-variable linear equation is stated in the customary form Ax + By = C. In this equation, A and B are coefficients, whereas C is a constant.
A linear equation is defined as follows:
A linear equation is one that has a maximum degree of one. This means that no variable in a linear equation that has an exponent will be greater than 1. The graph of every linear equation is always a straight line. A linear equation is an algebraic equation in which each term has an exponent of one and when graphed produces a straight line. This is why it is referred to as a ‘linear equation.’ There are one-variable linear equations and two-variable linear equations.
As a consequence, the linear equation formula is y = mx + b, with variables x and y. b represents the y-intercept and m is the slope of a line.
Standard Form Linear Equations:
Ax + B = 0 is the standard or general form of linear equations in one variable, where A and B are real values and x is the single variable. Ax + By = C is the conventional form of a two-variable linear equation, where A, B, and C are any real numbers, and x and y are the variables.
Derivation of Formula for Linear Equation:
Let’s look at the linear equation formula on a graph in the form of a straight line or slope. A slope is a line that represents the ratio of y-coordinate change to x-coordinate change.
y = mx + b the standard form of the equation for a straight line.
Where m is the line’s slope, b is the y-intercept, and x and y are the x- and y-axis coordinates, respectively.
The x-coordinate is equal to zero when the straight line is parallel to the x-axis. As a result, y = b
The y-coordinate will be 0 when the straight line is parallel to the y-axis. Therefore,
mx + b = 0
x = -b/m
As a result, the slope represents both the elevation of a line in the plane and the distance travelled along the x-axis.
To form a linear equation
To form a linear equation, follow the below step
- Step 1: Determine the Slope,
- Step 2: find out the y-intercept(b)
- Step 3: Write it in standard form
- Step 4: check the derived equation Is one degree.
Conclusion:
A linear equation is similar to any other equation in that two expressions are equal. One or two variables are used in linear equations. All right points lie on the same line when substituting values for the variables in a genuine linear equation and graphing the coordinates. For a basic slope-intercept linear equation, the slope and y-intercept must be determined first. Before developing a linear equation, use a line already drawn on a graph and its illustrated points.
