Question

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 \( 5 \).