Write y−2=3/2(x+2) in slope-intercept form.(1 point)

Question

Responses

y=3/2x+3/2
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=3/2x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=3/2x+6
y equals Start Fraction 3 over 2 End Fraction x plus 6

y=3/2+5x

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: \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] \[ y - 2 = \frac{3}{2}x + 3 \]

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

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

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