Question

Write y−2=3/2(x+2) in slope-intercept form.(1 point) Responses y=3/2x+6 y equals Start Fraction 3 over 2 End Fraction x plus 6 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=3/2+5x

Answer 1

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form (which is \( y = mx + b \)), we will solve for \( y \).

1. Start with the original equation: \[ y - 2 = \frac{3}{2}(x + 2) \]

2. Distribute \( \frac{3}{2} \) on the right side: \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] \[ y - 2 = \frac{3}{2}x + 3 \]

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

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