Given the line 3x + 4y + 10 = 0 find the angle wich it makes with the axis of x an its intercepts upon the axis.

We'll write the equation of the line into the standard
form.

y = m x + n, where m is the slope and n is the y
intercept.

We know that m = tan a, where a is the angle
made by the line with the axis of X.

We'll re-write the
equation of the line:

y = tan a*x +
n

We'll put the equation 3x + 4y + 10 = 0 in the standard
form. For this reason, we'll isolate 4y to the left side. We'll subtract 3x + 10 both
sides:

4y = -3x - 10

We'll
divide by 4:

y = -3x/4 -
10/4

y = -3x/4 - 5/2

The angle
made by the line with the axis of X is m = tan a.

We'll
identify m = -3/4

tan a =
-3/4

a = arctan (-3/4) +
k*pi

a = - arctan (3/4) +
k*pi

The x intercept of the line is found when y =
0

But y = -3x/4 - 5/2

-3x/4 -
5/2 = 0

We'll add 5/2 both
sides:

-3x/4 = 5/2

We'll cross
multiply and we'll get:

-6x =
20

We'll divide by -6:

x =
-20/6

x =
-10/3

So the line is intercepting x axis in
the point (-10/3 , 0).

When the line is
intercepting y axis, x = 0

So, y intercept is
n = -5/2.

So the line is
intercepting y axis in the point (0 , -5/2).