Question

1. l1: (0, 3) and (3, 1) l2: (-1, 4) and (-7, -5) parallel perpendicular neither slope l1 = ____ slope l2 = ____

Explanation:

Step1: Calculate slope of L1

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For L1 with points $(0, 3)$ and $(3, 1)$, $x_1 = 0, y_1 = 3, x_2 = 3, y_2 = 1$.
So slope of L1: $\frac{1 - 3}{3 - 0} = \frac{-2}{3} = -\frac{2}{3}$

Step2: Calculate slope of L2

For L2 with points $(-1, 4)$ and $(-7, -5)$, $x_1 = -1, y_1 = 4, x_2 = -7, y_2 = -5$.
Slope of L2: $\frac{-5 - 4}{-7 - (-1)} = \frac{-9}{-6} = \frac{3}{2}$

Step3: Check parallel or perpendicular

Parallel lines have equal slopes, perpendicular lines have slopes whose product is -1.
Product of slopes: $-\frac{2}{3} \times \frac{3}{2} = -1$. So they are perpendicular.

Answer:

Slope L1 = $-\frac{2}{3}$
Slope L2 = $\frac{3}{2}$
The lines are Perpendicular.