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The standard form of a linear equation in two variables, x and y, is
ax + by = k1 where a, b and k1 are constants.
This can be extended to three dimensions (x, y and z) simply:
ax + by + cz = k2 where a, b, c and k2 are constants.
Extension to 4 or more dimensions can be carried out in a similar way.
Apart from the fact that this form lends itself to simple extension to multi-dimensional space, the other main advantage is that the form is easy to represent in matrix form:
Thus AX = K where A is the matrix of coefficients, X the matrix of variables and k the matrix of constants. The tools of matrix algebra can then be used to work with these lines in hyperspace.
The standard form is sometimes confused with the slope-intercept form
y = ax + b.
What else can I help you with?
What is the standard from of a linear equation?
A linear equation is that equation in which a variable or variables has exponent equal to 1. For example, standard form of linear equation in one variable: a1x + a2x +.......+ anx = c Standard form of a linear equation : a1x + a2x +.........+ anx = c e.g. 4x + 3 =6, 3x + 6y + 5z = 2 etc.
Is 2x equals 7 in standard form or slope-intercept form?
Standard. You need a linear equation in two variables for slope-intercept form.
What is standard form linear equation's?
A standard form of a linear equation would be: ax + by = c
How do you do standard form of a linear equation if there is not a c?
aX+bY+cZ=0 Is a type of linear equation.
What are the importance of linear equation?
They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.
What is the standard form of linear function?
The standard form of a linear equation in n variables is a1x1 + a2x2 + ... + anxn = b. The ai and b are constants and the xi are variables.
What is the standard from of a linear equation?
A linear equation is that equation in which a variable or variables has exponent equal to 1. For example, standard form of linear equation in one variable: a1x + a2x +.......+ anx = c Standard form of a linear equation : a1x + a2x +.........+ anx = c e.g. 4x + 3 =6, 3x + 6y + 5z = 2 etc.
Is 2x equals 7 in standard form or slope-intercept form?
Standard. You need a linear equation in two variables for slope-intercept form.
What is standard form linear equation's?
A standard form of a linear equation would be: ax + by = c
What is standard form in a linear equation?
ax+by = c where a,b,c are constants and x,y are variables.
Which is the correct form for a linear equation?
The general form is for a linear equation in n variables is SUM aixi = b (i = 1,2,3,...,n) where xi are the variables and the ai are constant coefficients.
How do you do standard form of a linear equation if there is not a c?
aX+bY+cZ=0 Is a type of linear equation.
What are the importance of linear equation?
They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.
The standard form of linear equation?
Ax+By=C
What is the standard form of a linear equation?
Ax + By = C
Is 7xy-11 a linear equation?
No, the expression (7xy - 11) is not a linear equation because it contains the product of two variables, (x) and (y). A linear equation in two variables typically has the form (Ax + By + C = 0), where the variables are not multiplied together. In this case, the presence of the term (xy) indicates that the equation is nonlinear.
What is the standard form of an equation?
The standard form of an equation is Ax + By = C. In this type of equation, x and y are variables while A, B, and C are integers.
