writing linear eqautions from standard form to slope-intercept form

Question

9x-3y=12

Answer 1

To convert the linear equation from standard form \(Ax + By = C\) to slope-intercept form \(y = mx + b\), we can follow these steps:

Given the equation: \[ 9x - 3y = 12 \]

1. Isolate the y-term: Start by moving the \(x\) term to the right side of the equation. \[ -3y = -9x + 12 \]

2. Divide by the coefficient of y: To solve for \(y\), divide everything by \(-3\). \[ y = \frac{-9}{-3}x + \frac{12}{-3} \]

3. Simplify: Simplify the fractions. \[ y = 3x - 4 \]

So, the slope-intercept form of the equation \(9x - 3y = 12\) is: \[ y = 3x - 4 \]

Here, the slope \(m\) is 3, and the y-intercept \(b\) is -4.