Let's solve the problem step by step.

We need to find the slopes of the two lines and then determine their relationship (parallel, perpendicular, or intersecting). The slope formula for a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Line 1: Points (15, 20) and (17, 18)

The slope $m_1$ of Line 1 is:

$m_1 = \frac{18 - 20}{17 - 15} = \frac{-2}{2} = -1$

Line 2: Points (-22, -18) and (-20, -16)

The slope $m_2$ of Line 2 is:

$m_2 = \frac{-16 - (-18)}{-20 - (-22)} = \frac{-16 + 18}{-20 + 22} = \frac{2}{2} = 1$

Relationship between the lines

• If the slopes are equal, the lines are parallel.
• If the product of the slopes is $-1$, the lines are perpendicular.
• Otherwise, they are intersecting.

For Line 1, $m_1 = -1$, and for Line 2, $m_2 = 1$. The product of the slopes is:

$m_1 \times m_2 = -1 \times 1 = -1$

Since the product is $-1$, the lines are perpendicular.

Would you like more details or have any questions? Here are some related questions to explore further:

1. What is the equation of Line 1 in slope-intercept form?
2. What is the equation of Line 2 in slope-intercept form?
3. How do you find the point of intersection between two lines?
4. Can two perpendicular lines ever be parallel?
5. What is the significance of the negative reciprocal in determining perpendicularity?

Tip: Perpendicular lines have slopes that are negative reciprocals of each other.