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).

1.

The parallel lines have the same a slope.

We have:

Therefore, the searched line has the equation:

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

2.

Let and

The line l is perpendicular to the line k if and only if

We have

The searched line has the equation:

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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction