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Question

Slope-Intercept Form Quick Check
2 of 52 of 5 Items
Question
Write y−2=32(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+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=32x+5

Answer 1

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form, 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 solve for \(y\): \[ y = \frac{3}{2}x + 3 + 2 \] \[ y = \frac{3}{2}x + 5 \]

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

The correct response from the options given is:

• y = \(\frac{3}{2}\) x + 5