Question

Change the statement from standard form to slope-intercept form. Identify the slope and
y-intercept.
4x+3y=12

Answer 1

To convert the equation from standard form \(4x + 3y = 12\) to slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, follow these steps:

1. **Isolate \(y\)**: Start by moving the \(4x\) term to the right side of the equation.
\[
3y = -4x + 12
\]

2. **Solve for \(y\)**: Divide every term by \(3\) to solve for \(y\).
\[
y = -\frac{4}{3}x + 4
\]

Now the equation is in slope-intercept form:

\[
y = -\frac{4}{3}x + 4
\]

### Identifying the slope and y-intercept:
- **Slope (\(m\))**: \(-\frac{4}{3}\)
- **Y-intercept (\(b\))**: \(4\)

Thus, in slope-intercept form, the slope is \(-\frac{4}{3}\) and the y-intercept is \(4\).