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The general form of the equation of the straight line is \(ax + by + c = 0\).
Here, the coefficient of \(x = a\).
Coefficient of \(y = b\).
Constant term \(= c\).
The equation \(ax + by + c = 0\) can be written as:
\(y = -\frac{a}{b}x - \frac{c}{b}\) where \(b \neq 0\)
Here, the slope is \(m = -\frac{a}{b}\), and the \(y\)-intercept is \(-\frac{c}{b}\).
That is, Slope \(m = - \frac{\text{Coefficient of x}}{\text{Coefficient of y}}\) and \(y\)-intercept is \(-\frac{\text{Constant term}}{\text{Coefficient of y}}\)
Example:
Find the slope and \(y\)-intercept of the straight line \(3x + 9y - 6 = 0\).
Solution:
The given equation of the line is \(3x + 9y - 6 = 0\).
We know that Slope \(m = - \frac{\text{Coefficient of x}}{\text{Coefficient of y}}\) and \(y\)-intercept is \(-\frac{\text{Constant term}}{\text{Coefficient of y}}\)
Here, the Coefficient of \(x = 3\), Coefficient of \(y = 9\) and Constant term \(= - 6\)
Thus, Slope \(m = -\frac{3}{9} = - \frac{1}{3}\)
\(y\)-intercept \(= - \frac{(-6)}{9} = \frac{2}{3}\)
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