Find the equation of the straight line which makes angle 30 with positive direction of x axis and cuts intercepts +5 on the y axis .

Because, from the enunciation, we have information about
the slope and the y intercept, we'll put the equation into the standard
form:

y = mx + n

m - slope of
the line

n - y
intercept

Because we know the inclination of the line, a =
30 degrees, we could calculate the slope:

m = tan
30

m = sqrt 3/3

From
enunciation, we know that n = 5.

We'll write the equation
of the line:

y = (sqrt 3/3)*x +
5

We'll re-write the equation in the general
form:

3y - (sqrt3)*x - 15 =
0