Question

Change the statement from standard form to slope-intercept form. Identify the slope and
y-intercept.
3x-2y<-6

Answer 1

To convert the inequality \(3x - 2y < -6\) from standard form to slope-intercept form (which is \(y = mx + b\)), follow these steps:

1. **Isolate \(y\)** on one side of the inequality.

Start with the inequality:
\[
3x - 2y < -6
\]

2. **Subtract \(3x\)** from both sides:
\[
-2y < -3x - 6
\]

3. **Divide by -2** to solve for \(y\)**. Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign:
\[
y > \frac{3}{2}x + 3
\]

Now, this is in slope-intercept form (\(y = mx + b\)).

4. **Identify the slope and y-intercept:**
- The slope \(m = \frac{3}{2}\)
- The y-intercept \(b = 3\)

In summary:
- The inequality \(3x - 2y < -6\) rewritten in slope-intercept form is
\[
y > \frac{3}{2}x + 3
\]
- The slope is \(\frac{3}{2}\) and the y-intercept is \(3\).