Change the statement from standard form to slope-intercept form. Identify the slope and

Question

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 \(3\).