a. What is the equation of a horizontal line that passes through the point at
   (-2,-3) ?
b. Solve the system of equations:
   3x + y = 3
    x +2y= -4
c. What are the coordinates of the image of the point at (-3,-5) after a  
   reflection over the y-axis?
d. Find the measure of an angle if its measure is four times the
measure of its complement.

Hi teatea!
Here are the answers to your questions.

a. The general equation for a line can be expressed as:

y = m*x + b
where m and b are constants.

The constant 'm' represents the slope of the line and the constant 'b'
represents the intercept of the line.

Linear function, Slope-Intercept form
http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/lsif.html

The slope represents by how much y increases when x increases 1 unit.
In this case, since it's an horizontal line, y doesn't increase as x
increases. Therefore, we know that the slope is 0 (m=0). Now, the
intercept represent at what point the line crosses the y-axis. Since
this is an horizontal line that passes through (-2,-3), it's clear
that it will cross the y-axis at -3. Therefore, b=-3. So the equation
for this horizontal line is:

y = 0*x 3
  = 3


b. In order to solve this system, we can isolte one of the variables
in one of the equations and substitute in the other one. Thus we have:

x +2y= -4
x = -4 - 2y

The other equation is

3x + y = 3

So, substituting the x we found before into this equation we get:
3*(-4-2y) + y = 3
-12 -6y + y = 3
-5y = 15
  y = 15/(-5)
  y = -3

So we know that y=-3. In order to find x, we just plug this value into
any of the equations:

x = -4 - 2y
x = -4 - 2*(-3)
x = 2

The answer is x=2, y=-3


c. Let's see this graphically:

             |
             |
             |
             |
-----+-------+--------+------
     -3      |        3
             |
             |
             |
     x       |        o
  (-3,-5)    +-5    (3,-5) 
             |

The point stated in the problem is (-3,-5), labbeled with an x in this
graph. Since the y-axis is the vertical one, the reflection of this
point should be at the same "vertical" position but on the other side
of the y-axis. Therefore, the reflection of this point is at (3,-5)


d. Two angles are said to be complementary if their sum is 90º:

Angle Facts of Geometry
http://www.mathsteacher.com.au/year9/ch18_geometry/01_angle/facts.htm

So we have two pieces of information in this problem. Let's call xº to
the "first" angle and yº to the "second" one (of course, it doesn't
matter which we choose to be first or second). We know, fromthe fact
that they are complementary that:

xº + yº = 90º

Furthermore, we know that one of them is four times the other one. Thus,

xº = 4*yº

So what we have is a system of two equations. We solve it using the
same procedure as before: by substitution.

4*yº + yº = 90º
     5*yº = 90º
       yº = 90º/5
       yº = 18º

Finally,

xº = 4*yº
xº = 4*18º
xº = 72º

So the answer is that one of the angles' measure is 72º and the other one is 18º.


Google search strategy
complement angles geometry
slope intercept line


I hope this helps! If you have any dosubts regarding my answer, please
don't hesitate to request a clarification before rating it. Otherwise
I await your rating and final comments.

Best wishes!
elmarto