Write y - 2 = 3/2 (x + 2) in slope intercept form

Answer 1

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form (which is \( y = mx + b \)), follow these steps:

1. Distribute \(\frac{3}{2}\) on the right side:

   \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \]

   This simplifies to:

   \[ y - 2 = \frac{3}{2}x + 3 \]

2. Next, solve for \( y \) by adding 2 to both sides:

   \[ y = \frac{3}{2}x + 3 + 2 \]

   This simplifies to:

   \[ y = \frac{3}{2}x + 5 \]

The equation in slope-intercept form is:

\[ y = \frac{3}{2}x + 5 \]

Here, the slope \( m \) is \(\frac{3}{2}\) and the y-intercept \( b \) is \( 5 \).