Write y−2=3/2(x+2)

Question

in slope-intercept form.(1 point)
Responses

y=32x+6
y equals Start Fraction 3 over 2 End Fraction x plus 6

y=32x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=32x+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=32+5x

Answer 1

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

1. Distribute the \(\frac{3}{2}\) on the right side:

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

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

2. Now, add 2 to both sides to solve for \(y\):

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

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

So the equation in slope-intercept form is:

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

Therefore, the correct response is:

y = \frac{3}{2}x + 5.