Slope Intercept Form of a Line - Calculator

This online calculator rewrites an equation of a line of the general form \[ a x + b y = c \] into the slope intercept form \[ y = m x + B\]

Rewrite the Equation of a Line in Slope Intercept Form

The importance of the slope intercept form of a line lies in the fact that the slope \( m \) and the y intercept \( B \) of the line are easily identified and here are the steps to follow:

1) Solve the general equation \( a x + b y = c \) for \( y \) \[ b y = - a x + c \] for \( b \) not equal to zero, we divide all terms by the coefficient \( b \). \[ y = -\frac{a}{b}x + \frac{c}{b} \] 2) Compare the above equation to the slope intercept form \( y = m x + B \) and identify \( m \) and \( B \) as \[ m = -\frac{a}{b} \quad \text{and} \quad B = \frac{c}{b} \]

Numerical Example

Find slope and the y intercept of the line given by the equation \[ 2 y + 3 x = 6 \]

Solution to the Numerical Example

Solve the equation for \( y \) \[2 y = - 3 x + 6 \] \[ y = - (3/2) x + 3 \] Compare the above equation to the slope intercept for \( y = m x + B \) to find the slope \[ m = - 3 / 2 \] and the y intercept \[ B = 3 \]

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