Question

in the following, lines k and w pass through the given points: k: goes through points (2, 3) & (4, 4) w: goes through (3, 6) & (-7, 1) determine if lines k and w are parallel, perpendicular, or neither. hint: find slopes using m = (y2 - y1)/(x2 - x1)

Explanation:

Step1: Calculate slope of line k

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For line k with points $(2,3)$ and $(4,4)$, $x_1 = 2,y_1 = 3,x_2 = 4,y_2 = 4$. Then $m_k=\frac{4 - 3}{4 - 2}=\frac{1}{2}$.

Step2: Calculate slope of line w

For line w with points $(3,6)$ and $(- 7,1)$, $x_1 = 3,y_1 = 6,x_2=-7,y_2 = 1$. Then $m_w=\frac{1 - 6}{-7 - 3}=\frac{-5}{-10}=\frac{1}{2}$.

Step3: Determine relationship

Since $m_k=m_w=\frac{1}{2}$, the lines are parallel.

Answer:

The lines k and w are parallel.