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The image shows two equations of lines \(7y = 3x + 7\) and \(6y + 14x = -20\). To determine if the lines are parallel, perpendicular, or neither, we need to rewrite these equations in slope-intercept form \(y = mx + b\), where \(m\) represents the slope.

1. For the first equation \(7y = 3x + 7\):
   \[
   y = \frac{3}{7}x + 1
   \]
   The slope of this line is \(\frac{3}{7}\).

2. For the second equation \(6y + 14x = -20\), first isolate \(y\):
   \[
   6y = -14x - 20 \implies y = -\frac{7}{3}x - \frac{10}{3}
   \]
   The slope of this line is \(-\frac{7}{3}\).

The slopes \(\frac{3}{7}\) and \(-\frac{7}{3}\) are negative reciprocals, which means the lines are **perpendicular**.

The correct answer is: **B. The two lines are perpendicular**.

Do you want further details or have any other questions?

Here are 5 related questions you might find interesting:
1. How can we determine if two lines are parallel from their slopes?
2. What are the conditions for two lines to be neither parallel nor perpendicular?
3. How would the solution change if one of the lines was vertical or horizontal?
4. Can two lines be both parallel and intersecting at one point?
5. How do we graphically represent perpendicular lines?

**Tip:** When working with linear equations, converting them into slope-intercept form \(y = mx + b\) is often the quickest way to identify key features like slope and intercepts.

Using the two equations of the lines 7y=3x+7 and 6y +14x=-20, determine if the lines are parallel, perpendicular, or neither.

Learn how to determine whether two lines given by the equations 7y=3x+7 and 6y +14x=-20 are parallel, perpendicular, or neither. This problem focuses on key algebraic concepts, including slope-intercept form and the perpendicular line theorem. Ideal for students in Grades 8-10.

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