Find the equation of the line passing through (3,2) and parallel to 3x+y=-3. Answer in slope intercept form

To find the equation of the line passing through \((3, 2)\) and parallel to the line \(3x + y = -3\), we can follow these steps:

### Step 1: Find the slope of the given line.
We start by converting the equation \(3x + y = -3\) into slope-intercept form \((y = mx + b)\), where \(m\) is the slope.

\[
3x + y = -3
\]
Subtract \(3x\) from both sides:
\[
y = -3x - 3
\]
Now, the equation is in slope-intercept form, and the slope \(m = -3\).

### Step 2: Use the point-slope form.
Since the new line is parallel to the given line, it will have the same slope, \(m = -3\). The equation of a line in point-slope form is:

\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope. Using the point \((3, 2)\) and the slope \(m = -3\):

\[
y - 2 = -3(x - 3)
\]

### Step 3: Simplify to slope-intercept form.
Now expand and simplify:

\[
y - 2 = -3x + 9
\]
Add 2 to both sides:
\[
y = -3x + 11
\]

### Final Answer:
The equation of the line is:
\[
y = -3x + 11
\]

Would you like a more detailed breakdown of any steps, or do you have any further questions?

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Here are five related questions to expand on this topic:
1. How would you find the equation of a line perpendicular to \(3x + y = -3\)?
2. Can you derive the equation of a line given its slope and any other point on the line?
3. How does the slope of parallel and perpendicular lines relate?
4. How would you determine the x- and y-intercepts of the line \(y = -3x + 11\)?
5. How do you graph the line \(y = -3x + 11\) on a coordinate plane?

**Tip:** When two lines are parallel, their slopes are always equal!

Find the equation of the line passing through (3,2) and parallel to 3x+y=-3. Answer in slope intercept form.

Learn how to find the equation of a line passing through the point (3,2) that is parallel to the line 3x + y = -3. This solution includes key concepts from algebra such as slope-intercept form and parallel lines. Suitable for students in Grades 8-10.

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