Question

what is the slope of line pq? what is the slope of line mn? how are the two lines related? graph: coordinate plane with x-axis (-10 to 10) and y-axis (-10 to 10), grid lines. point p at (-8, 2), q at (4, 2) (orange line pq). point m at (8, 6), n at (8, -8) (blue line mn).

Explanation:

Slope of line PQ:

Step1: Identify coordinates of P and Q

Point P is at \((-8, 2)\) and point Q is at \((4, 2)\).

Step2: Use slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = -8\), \(y_1 = 2\), \(x_2 = 4\), \(y_2 = 2\) into the formula:
\(m_{PQ} = \frac{2 - 2}{4 - (-8)} = \frac{0}{12} = 0\).

Slope of line MN:

Step1: Identify coordinates of M and N

Point M is at \((8, 6)\) and point N is at \((8, -8)\).

Step2: Use slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = 8\), \(y_1 = 6\), \(x_2 = 8\), \(y_2 = -8\) into the formula:
\(m_{MN} = \frac{-8 - 6}{8 - 8} = \frac{-14}{0}\), which is undefined (vertical line).

Relationship between PQ and MN:

• Line PQ has a slope of \(0\) (horizontal line, \(y = 2\)).
• Line MN has an undefined slope (vertical line, \(x = 8\)).
• A horizontal line and a vertical line intersect at \(90^\circ\), so they are perpendicular.

Answer:

s:

• Slope of PQ: \(0\)
• Slope of MN: Undefined
• Relationship: Perpendicular (or "PQ is horizontal, MN is vertical, and they are perpendicular")