Line l in the figure below is parallel to the line y = 4 x + 1. find the coordinates of the point p

If L is parallel to y = 4x + 1, then L must have the same slope.  Thus, L has the form y = 4x + b

To figure out what "b" is, it is shown that point (0, -2) is on line L.  So plug that into y = 4x + b, and we will see that b has to be equal to -2.  Thus our equation of L is: y = 4x - 2

Now since P is a x-intercept, it has the coordinates: (x,0).

To figure out what x is, we need to solve:

0 = 4x - 2, solve:

2 = 4x

2/4 = x

1/2 = x

Thus point P is (1/2,0)