Question

Please help me,I give up on this.i just don’t get it.

Answer 1

1. 
   `y = -(4)/(5) x - (14)/(5)`
2. 
   `y = (5)/(4) x -11`

Explanation:

Given line ;

`y = (5)/(4) x -3\\\\m = slope\\m = (5)/(4)`

1. Perpendicular and passes through (4,-6)

`m_1 = (5)/(4) \\\\m_2 = (-1)/(m_1) \\\\m_2 = (-1)/((5)/(4) ) \\\\m_2 = -(4)/(5) \\\\(4,-6)=(x ,y)\\`

Substitute the values above into slope intercept form ; y=mx+b and solve for b.

`y =mx+b\\\\-6 = -(4)/(5) (4) + b\\\\-6 = -(16)/(5) + b\\\\-6 + (16)/(5) = b\\\\-(14)/(5) = b\\\\b = -(14)/(5)\\\\m = - (4)/(5)`

Substitute new values into ; y =mx+b.

`y = -(4)/(5) (x)- ((14)/(5) )\\\\y = -(4)/(5) x - (14)/(5)`

2.Parallel and passes through (4,-6)

`m = (5)/(4) \\\\(4,-6)=(x_1,y_1)`

Substitute values into point slope form and simplify

`y-y_1=m(x-x_1)\\\\y - (-6) = (5)/(4) (x -4)\\\\y+6 = (5)/(4) x -5\\\\y = (5)/(4) x -5-6\\\\y = (5)/(4) x -11`