Question

writing linear eqautions from standard form to slope-intercept form
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.