The standard form is another way to write the equations. We have many kinds of standard forms of the formulas used in Algebra.
For example, the standard form 3x^2 – 7 + 4x^3 + x^5 is x^5 +4x^3 +3 x^2 – 7. We know the standard form of a quadratic equation is ax^2 + box =c = 0, here we have a condition that is a ≠ 0. We have intercept form and slope intercept forms to write a line in standard forms.
Intercept form of a line is: (x /a) + (y/b) = 1
Here, a and b are x and y intercepts
Slope – intercept form of a line: y = mx + c
Here, m is the slope and c is the y intercept.
Example 1: Write the equation of a line 3x + 4y = 12 in intercept form.
Solution: We know the intercept form of a line that is x/a + y/b = 1
The given equation is 3x + 4y = 12
To write this in the form, we need to divide by 12
(3x/12) + (4y/12) = (12/12)
( x/4 ) + (y/3) = 1
Here, 4 is the x intercept and 3 is the y intercept.
Example 2: Write the equation 6x + 2y – 6 = 0.
Solution: We know the slope-intercept form of a line that is y = mx + c
The given equation is 6x + 2y – 6 =0
2y = -6x + 6
y = - 3x + 3
Here, -3 is the slope of the line and 3 is the y intercept.