Question

For what value of p will the equations be parallel? Y=Px-6, 4y+1=(p-2)x-3

Answer 1

Answer:

p = $-\frac{2}{3}$  

Step-by-step explanation:

Lines are parallel if slopes are the same and y-intercepts are different.

$l_{1}$ : y = $m_{1}$ x + $b_{1}$ ,

$l_{2}$ : y = $m_{2}$ x + $b_{2}$

$l_{1}$ ║ $l_{2}$ if $m_{1}$ = $m_{2}$ , $b_{1}$ ≠ $b_{2}$

~~~~~~~~~~~~~~~~

$l_{1}$ : y = px - 6

$l_{2}$ : 4y + 1 = (p - 2)x - 3 ⇔ 4y = (p - 2)x - 4 ⇔ y = $\frac{p-2}{4}$ x - 1

p = $\frac{p-2}{4}$ ⇔ 4p = p - 2 ⇒ p = $-\frac{2}{3}$