write an equation parallel to the equation 3x-2y=7

To find an equation that is parallel to \( 3x - 2y = 7 \), we need to ensure that the new equation has the same slope. Here are the steps:

1. Rewrite the given equation in slope-intercept form (\(y = mx + b\)), where \(m\) represents the slope:
   \[
   3x - 2y = 7
   \]
   Solve for \(y\):
   \[
   -2y = -3x + 7
   \]
   \[
   y = \frac{3}{2}x - \frac{7}{2}
   \]
   The slope is \(m = \frac{3}{2}\).

2. A line parallel to this one must have the same slope, \(m = \frac{3}{2}\), but a different \(y\)-intercept. So, the equation of a parallel line will be:
   \[
   y = \frac{3}{2}x + b
   \]
   where \(b\) is any constant different from \(-\frac{7}{2}\).

For example, a parallel line could be:
\[
y = \frac{3}{2}x + 4
\]
Or in standard form:
\[
3x - 2y = -8
\]
This is one possible equation parallel to the original.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line from its equation?
2. What is the difference between parallel and perpendicular lines?
3. How do you convert from slope-intercept form to standard form?
4. Can you find an equation perpendicular to \(3x - 2y = 7\)?
5. How do changes in the \(y\)-intercept affect the graph of a line?

**Tip:** Parallel lines have identical slopes but different intercepts, while perpendicular lines have slopes that are negative reciprocals.

Learn how to find an equation parallel to 3x - 2y = 7. This problem involves key algebraic concepts such as slope-intercept form and the properties of parallel lines. A step-by-step solution ensures understanding for students in Grades 8-10.

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