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The problem asks to find the equation of a line that is parallel to the given line and passes through the point \( (3, -1) \).

### Step 1: Find the slope of the given line
The given line is in standard form:  
\[
8x - 3y = 5
\]

We need to rewrite this in slope-intercept form \( y = mx + b \) to find the slope.

First, solve for \( y \):
\[
-3y = -8x + 5
\]
\[
y = \frac{8}{3}x - \frac{5}{3}
\]
The slope \( m \) of this line is \( \frac{8}{3} \).

### Step 2: Write the equation of the parallel line
Parallel lines have the same slope, so the slope of the new line is also \( \frac{8}{3} \).

We use the point-slope form to find the equation of the line passing through \( (3, -1) \):
\[
y - y_1 = m(x - x_1)
\]
where \( m = \frac{8}{3} \), \( (x_1, y_1) = (3, -1) \). Substituting the values:
\[
y - (-1) = \frac{8}{3}(x - 3)
\]
\[
y + 1 = \frac{8}{3}(x - 3)
\]

### Step 3: Simplify the equation
Distribute the slope on the right side:
\[
y + 1 = \frac{8}{3}x - 8
\]
Subtract 1 from both sides:
\[
y = \frac{8}{3}x - 9
\]

Thus, the equation of the line parallel to \( 8x - 3y = 5 \) and passing through \( (3, -1) \) is:
\[
y = \frac{8}{3}x - 9
\]

Let me know if you'd like more details or have any questions!

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Here are 5 related questions for practice:
1. What is the equation of a line parallel to \( 2x - y = 4 \) and passing through \( (5, 2) \)?
2. How would the equation change if the new line was **perpendicular** to the original line?
3. Find the slope of a line perpendicular to the line \( 4x + 5y = 10 \).
4. How do you convert an equation from standard form to slope-intercept form?
5. What is the equation of a line passing through \( (-2, 3) \) and parallel to \( y = -\frac{1}{2}x + 6 \)?

### Tip:
For parallel lines, always remember that they share the same slope. For perpendicular lines, their slopes are negative reciprocals of each other.

Write an equation of a line containing the given point and parallel to the given line: (3, -1); 8x - 3y = 5.

Learn how to write the equation of a line parallel to 8x - 3y = 5 that passes through the point (3, -1). This step-by-step solution includes slope-intercept form, point-slope form, and key algebraic concepts. Suitable for Grades 7-9.

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