Question

Question

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

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

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

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

Answer 1

To write the equation \( y - 2 = \frac{3}{2}(x + 2) \) in slope-intercept form (which is \( y = mx + b \)), let's start by distributing and simplifying the equation.

1. Distribute \( \frac{3}{2} \): \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] Simplifying \( \frac{3}{2} \cdot 2 \) gives: \[ y - 2 = \frac{3}{2}x + 3 \]

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

From the provided responses, the correct response is: \[ y = \frac{3}{2}x + 5 \]