Question

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

Answer 1

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) to slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to isolate \( y \).

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. Now, add 2 to both sides to isolate \( y \):
\[
y = \frac{3}{2}x + 3 + 2
\]
\[
y = \frac{3}{2}x + 5
\]

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

Here, the slope \( m \) is \( \frac{3}{2} \) and the y-intercept \( b \) is \( 5 \).