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We are asked to find which equation represents a line that passes through the point \( (6, -3) \) and is parallel to the graph of \( y = 3x + 1 \).

### Step 1: Identifying the Slope
The slope of the line \( y = 3x + 1 \) is 3, since the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. 

Since the new line is parallel, it will have the same slope, so the slope of the line we are looking for is also 3.

### Step 2: Using the Point-Slope Form
We will now use the point-slope form of a line equation, which is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Substituting \( m = 3 \), \( x_1 = 6 \), and \( y_1 = -3 \) into the equation:
\[
y - (-3) = 3(x - 6)
\]
Simplifying:
\[
y + 3 = 3(x - 6)
\]
\[
y + 3 = 3x - 18
\]
\[
y = 3x - 21
\]

### Step 3: Matching the Equation
The equation we found is \( y = 3x - 21 \), which matches option **A**.

### Final Answer:
The correct choice is **A**.

Do you want more details or have any questions?

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Here are 5 related questions you might find useful:
1. How do you find the slope of a line from its equation?
2. What is the point-slope form, and how is it used?
3. How can you determine if two lines are parallel?
4. What changes in the equation if the lines were perpendicular instead of parallel?
5. How do you convert from point-slope form to slope-intercept form?

**Tip:** When given a line and asked for a parallel line, remember that the slope stays the same!

Which equation represents a line that passes through the point (6, -3) and is parallel to the graph of y = 3x + 1?

Find the equation of a line passing through the point (6, -3) that is parallel to y = 3x + 1. Learn how to use point-slope and slope-intercept forms to solve linear equation problems. Suitable for Grades 8-10.

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