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