Question

Line AB passes through (-3,5) and (p, -7), and line CD passes through (3,-1) and (-4,5). For what

value of p, the lines AB and CD are parallel to each other?
Please help me ASPA I NEED THIS BY EVENING

Answer 1

p = 11

Explanation:

Let's start by finding the slope of line CD:

`Slope=(y_2-y_1)/(x_2-x_1)`

Plug in the given coordinates into the equation:

`Slope=(5-(-1))/(-4-3)=(5+1)/(-7)=-(6)/(7)`

Parallel lines have the same slope. This means we can plug the slope of line CD in to find p (in this case p is
`x_2`)...

`Slope=(y_2-y_1)/(x_2-x_1)`

`-(6)/(7)=(-7-5)/(p-(-3))\\-(6)/(7)=(-12)/(p+3)`

Cross multiply (multiply numerator of first fraction by denominator of second and vice versa):

`6(p+3)=(-7)(-12)`

Distribute:

`6p+18=84`

Subtract 18 from both sides:

`6p=66`

Divide both sides by 6

`p=11`