Question

1. find the equation of the line that is parallel to the line y=-3/2x+4 and passes through point (4,0).

2. find the equation of the line that is perpendicular to the line y=-1/3x-1 And passes through point (1,5).

Answer 1

1.

The parallel lines have the same a slope.

We have:

`y=-(3)/(2)x+4`

Therefore, the searched line has the equation:

`y=-(3)/(2)x+b`

We know, the line passes through point (4,0). Substitute the coordinates of the point to the equation of the line:

`0=-(3)/(2)(4)+b\\\\0=-(3)(2)+b\\\\0=-6+b\qquad|+6\\\\6=b\to b=6`

Answer:
`y=-(3)/(2)x+6`

2.

Let
`k:y=m_1x+b_1` and
`l:y=m_2x+b_2`

The line l is perpendicular to the line k if and only if
`m_1m_2=-1`

We have
`k:y=-(1)/(3)x-1`

`l:y=mx+b\\\\l\ \perp\ k\iff-(1)/(3)m=-1\qquad|\cdot(-3)\\\\m=3`

The searched line has the equation:
`y=3x+b`

We know, the line passes through point (1,5). Substitute the coordinates of the point to the equation of the line:

`5=3(1)+b\\\\5=3+b\qquad|-3\\\\2=b\to b=2`

Answer:
`y=3x+2`