Put the following equation of a line into slope-intercept form, simplifying all fractions.
\[
3 x-2 y=-2
\]
Answer
Attempt 1 out of 2
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Answer
Final Answer: The slope-intercept form of the given equation is \(\boxed{y = \frac{3}{2}x + 1}\).
Step 1 ：The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. To put the given equation into this form, we need to isolate \(y\). We can do this by adding \(2y\) to both sides of the equation and then dividing by \(2\).
Step 2 ：Starting with the equation \(3x - 2y = -2\), we add \(2y\) to both sides to get \(3x = 2y - 2\).
Step 3 ：Next, we divide both sides by \(2\) to isolate \(y\), giving us \(y = \frac{3}{2}x + 1\).
Step 4 ：Final Answer: The slope-intercept form of the given equation is \(\boxed{y = \frac{3}{2}x + 1}\).
