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

y = 3/2 + 5x

y = 3/2 * x + 5

y = 3/2 * x + 3/2

y = 3/2 * x + 6

1 answer

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

  1. Distribute the \( \frac{3}{2} \) on the right side of the equation: \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] This simplifies to: \[ y - 2 = \frac{3}{2}x + 3 \]

  2. Next, add 2 to both sides to solve for \( y \): \[ y = \frac{3}{2}x + 3 + 2 \] This simplifies to: \[ y = \frac{3}{2}x + 5 \]

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

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