Question

Determine whether the line Upper L 1L1 whose equation is yequals=5 x minus 95x−9 and the line Upper L 2L2 whose equation is yequals=one fifth x plus 6 1 5x+6 are​ parallel, perpendicular, or neither.

Answer 1

Answer:

Neither

Step-by-step explanation:

Let $m_{1}$ and $m_{2}$ be the gradients of two lines.

1. The two lines are parallel if their gradients $m_{1}$ and $m_{2}$ are equal.
2. Two lines are perpendicular if the products of the gradients, $m_{1}$$m_{2}$ =-1, i.e. gradient of one, $m_{1}=-\frac{1}{m_{2}}$ $m_{2}$

Consider the given lines $L_{1}$ whose equation is given as y=5x-9 and the line $L_{2}$ whose equation is given as $y=\frac{1}{5}x+6$.

To make a comparison, ensure that the lines are in the slope-intercept form y=mx+c.

In $L_{1}$ y=5x-9, $m_{1}$ =5

In $L_{2}$ , $y=\frac{1}{5}x+6$, $m_{2}$ =$\frac{1}{5}$

Their product $m_{1}$$m_{2}$ = 1,

Therefore the lines are neither parallel nor perpendicular.