Write y−2=3/2(x+2)

Question

in slope-intercept form.(1 point)
Responses

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

y=3/2x+32
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

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 \( y \): \[ y = \frac{3}{2}x + 3 + 2 \] \[ y = \frac{3}{2}x + 5 \]

Thus, the equation in slope-intercept form is:

\[ y = \frac{3}{2}x + 5 \]

The correct response is: y equals Start Fraction 3 over 2 End Fraction x plus 5.