Question

find the slopes of the lines ( l_1 ) and ( l_2 ) defined by the two given points. then determine whether ( l_1 ) and ( l_2 ) are parallel, perpendicular, or neither.

( l_1 ): ( (4, -1) ) and ( (3, -6) )
( l_2 ): ( (-3, 0) ) and ( (2, -1) )

progress: 0/3

part 1 of 3

the slope of ( l_1 ) is (\boxed{quad}).

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify points for \( l_1 \)

For \( l_1 \), the points are \((4, -1)\) (so \( x_1 = 4, y_1=-1 \)) and \((3, -6)\) (so \( x_2 = 3, y_2=-6 \)).

Step3: Calculate slope of \( l_1 \)

Substitute into the formula: \( m=\frac{-6 - (-1)}{3 - 4}=\frac{-6 + 1}{-1}=\frac{-5}{-1}=5 \).

Answer:

\( 5 \)