Question

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 8, 2) and (4, 2). Line M N has points (8, 6) and (8, negative 8). What is the slope of line PQ? What is the slope of line MN? How are the two lines related?

Answer 1

Answer:

Slope of PQ = 0

Slope of MN = infinity

PQ and MN are perpendicular to each other

Step-by-step explanation:

for any two points  (x1, y1),  (x2, y2)given in coordinate plane slope is given by

$y1 - y2/x1-x2\\\\For \ line \ PQ\\slope = 2 - 2/-8-4 = 0\\\\For \ line \ MN \\slope = 6 - (-8)/8-8 = 1/0 = infinity$

For any line if slope is zero it is parallel  to X axis and perpendicular to Y axis

For any line if slope is infinity it is parallel  to Y axis and perpendicular to X axis

Also we know X and Y are perpendicular to each other.

Since slope of PQ is zero it is parallel  to X axis and perpendicular to Y axis

Since slope of MN is infinity it is parallel  to Y axis and perpendicular to X axis.

Thus two lines PQ and MN are perpendicular to each other.

Answer 2

Answer

Given,

Points of the line PQ are (-8,2) and (4,2)

Slope of the line

$m_1 = \frac{y_2-y_1}{x_2-x_1}$

$m_1 = \frac{2-2}{4+8}$

$m_1 = 0$

Points of the line MM are (8,-6) and (8,-8)

Slope of the line

$m_2 = \frac{y_2-y_1}{x_2-x_1}$

$m_2 = \frac{2-2}{4+8}$

Line PQ is parallel to x-axis and pass through y = 2.

Line MN is parallel to y-axis and pass through x = 8.

Both line intersect at (8,2).