Write y−2=3/2(x+2)

Question

in slope-intercept form.(1 point)
Responses

y=3/2x+6

y=3/2+5x

y=3/2x+5

y=3/2x+3/2

Answer 1

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

1. Distribute \(\frac{3}{2}\) to both \(x\) and \(2\): \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] \[ y - 2 = \frac{3}{2}x + 3 \]

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

Thus, the equation in slope-intercept form is: \[ y = \frac{3}{2}x + 5 \]

The correct response is: y = \frac{3}{2}x + 5.