We will learn the transformation of general form into slopeintercept form.
To reduce the general equation Ax + By + C = 0 into slopeintercept form (y = mx + b):
We have the general equation Ax + By + C = 0.
If b ≠ 0, then from the given equation we get,
By =  Ax  C (Subtracting ax from both sides)
⇒ y=  A/Bx  C/B, [Dividing both sides by b (≠0).
⇒ y = (\(\frac{A}{B}\))x + (\(\frac{C}{B}\))
Which is the required slopeintercept form (y = mx + b) of the general form of line Ax + By + C = 0, where m = \(\frac{A}{B}\), b = \(\frac{C}{B}\)
Thus, for the straight line Ax + By + C = 0,
m = slope = \(\frac{A}{B}\) =  \(\frac{\textrm{Coefficient of x}}{\textrm{Coefficient of y}}\)
Note:
To determine the slope of a line by the formula m =  \(\frac{\textrm{Coefficient of x}}{\textrm{Coefficient of y}}\) first transfer all terms in the equation on one side.
Solved examples on transformation of general equation into slopeintercept form:
1. Transform the equation of the straight line 2x + 3y  9 = 0 to slope intercept form and find its slope and yintercept.
Solution:
The given equation of the straight line 2x + 3y  9 = 0
First subtract 2x from both sides.
⇒ 3y  9 = 2x
Now add 9 on both sides
⇒ 3y = 2x + 9
Then divide both sides by 3
⇒ y = (\(\frac{2}{3}\))x + 3, which is the required slopeintercept form of the given straight line 2x + 3y  9 = 0.
Therefore, slope of the given line (m) = \(\frac{2}{3}\) and yintercept = 3.
2. Reduce the equation 5x + 2y = 7 into slope intercept form and find its slope and yintercept.
Solution:
The given equation of the straight line 5x + 2y = 7.
Now solve for y in terms of x.
⇒ 2y = 5x + 7
⇒ y = (\(\frac{5}{2}\))x + \(\frac{7}{2}\), which is the required slopeintercept form of the given straight 5x + 2y = 7.
Therefore, slope of the given straight line \(\frac{5}{2}\) and yintercept \(\frac{7}{2}\).
`● The Straight Line
11 and 12 Grade Math
From General Form into Slopeintercept Form to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.