Question

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

Answer 1

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

1. Start with the given equation:
\[
y - 2 = \frac{3}{2}(x + 2)
\]

2. Distribute \( \frac{3}{2} \) on the right side:
\[
y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2
\]
\[
y - 2 = \frac{3}{2}x + 3
\]

3. Add 2 to both sides to isolate \( y \):
\[
y = \frac{3}{2}x + 3 + 2
\]
\[
y = \frac{3}{2}x + 5
\]

Now, the equation is in slope-intercept form, where the slope \( m = \frac{3}{2} \) and the y-intercept \( b = 5 \). Thus, the final answer is:
\[
y = \frac{3}{2}x + 5
\]