
Consider the graphed equation shown. What is the equation of the line that passes through (−3, 2) and is parallel to the graphed equation? 

To solve this problem, we need to follow these steps:

### 1. **Determine the slope of the given graphed equation.**
Since the new line is parallel to the given equation, it will have the same slope. Let’s assume that the equation of the graphed line is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. If you can provide the equation of the line or details about its slope (from a graph, for instance), we can use that slope for the new line.

### 2. **Use the slope for the new line.**
If the slope of the given line is \(m\), the slope of the new line will also be \(m\), as parallel lines share the same slope.

### 3. **Apply the point-slope form to find the new equation.**
We know the new line passes through the point \((-3, 2)\), so we can use the point-slope formula:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \(x_1 = -3\)
- \(y_1 = 2\)
- \(m\) is the slope (which is the same as the slope of the original line).

Substituting the values:

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

### 4. **Simplify the equation (if needed).**
Once you find the slope \(m\), you can simplify this equation into slope-intercept form \(y = mx + b\), or leave it in point-slope form.

If you can provide more information about the graphed line (either visually or as an equation), I can complete the equation for you.

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Do you want further details on finding the slope of a line or clarifications?  
Here are five related questions to expand the discussion:

1. How do you find the slope of a line from a graph?
2. What are the differences between parallel and perpendicular lines?
3. How do you convert between point-slope form and slope-intercept form?
4. What are the steps to find the equation of a line given two points?
5. How do changes in slope affect the steepness of a line?

**Tip:** When two lines are parallel, they never intersect, meaning they will always have the same slope!

Consider the graphed equation shown. What is the equation of the line that passes through (−3, 2) and is parallel to the graphed equation?

Learn how to find the equation of a line that passes through the point (-3, 2) and is parallel to a given graphed equation. This solution covers algebraic concepts such as slope, parallel lines, and the point-slope formula, suitable for Grades 8-10.

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