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

Question

A. y = 3/2x + 6
B. y = 3/2x + 3/2
C. y = 3/2 + 5x
D. y = 3/2x + 5

Answer 1

To write the equation \( y - 2 = \frac{3}{2} (x + 2) \) in slope-intercept form, we need to solve for \( y \).

1. Start with the original 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. Now, add \(2\) to both sides to solve for \(y\): \[ y = \frac{3}{2}x + 3 + 2 \] \[ y = \frac{3}{2}x + 5 \]

Now, the equation is in slope-intercept form \(y = mx + b\) where \(m = \frac{3}{2}\) and \(b = 5\).

Thus, the correct answer is: D. y = \frac{3}{2}x + 5