Standard form of Linear Equations in Two Variables
Standard form of Linear Equations in Two Variables
The Standard Form for a linear equation in two variables, x and y, is usually given as : ax + by = c, where a, b and c are real numbers, and a and b are not both zero.
If we have a linear equation in slope-intercept form, y = m x + b
For example, 3x + 2y = 8 is a linear equation in two variables.
Illustration: Convert 
in standard form :
Solution : The given equation, ,
We get , 3y - 8x = 15,
So as we know, ax + by = c is the standard form, the final answer is -8x + 3y = 15
Convert the Slope - Intercept form into Standard Form
So, to convert from slope intercept form y = mx + b to standard form ax + by + c = 0, let m = a/b.
Then collect all terms on the left side of the equation and multiply by the denominator b to get rid of the fraction.
The slope is defined to be the change in y divided by the change in x. Thus, if we express the slope as m = y change/x change or , we will have met our first demand.
Converting from slope intercept form to standard form takes little more than basic arithmetic.
An equation in slope intercept form has the basic structure
y=mx+b
y-mx=(mx-mx)+b
y-mx=b
y-mx-b=b-b
y-mx-b=0
−mx+y−b=0
If m is an integer, then B will equal 1.
Illustration:The equation of a line in slope intercept form is:
What is the equation in standard form?
Solution:
By comparing the linear equation - 5y + 2x + 8 =0 with ax + by + c = 0, find the value of c. | |||
| Right Option : B | |||
| View Explanation | |||
Which is the correct standard form of the linear equation
| |||
| Right Option : C | |||
| View Explanation | |||
What is a standard form of the linear equation 7x- 21 + 2y =0? | |||
| Right Option : D | |||
| View Explanation | |||
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