We have 2 cases:
passes through (2,-3) and parallel to x-axis,
Parallel to x-axis means that the slope = 0
==> y-y1= m(x-x1)
==> y+3 - 0
==> y= -3
Passes througth (-2, 3) and parallel to y-axis,
That means that the function does not intersect with y-axis then y values are unlimited:
Then the equation is:
==> x= -2
So, we have to write the equation of the line in 2 cases:
1) parallel to x axis;
2) parallel to y axis.
Let's write the equation of the line that passes through the point (2,-3) and is parallel to x axis.
We'll start from the standard form of the equation:
y = mx + n
The point (2,-3) is on the line if:
-3 = 2m + n
The line is parallel to x axis so their slopes have to be equals.
Since the slope of x axis is m=0, then the slope of the parallel line is also m=0
The equation of the line is :
-3 = 2*0 + n
n = -3
y = -3
2) When the line that passes through the point (2,-3) is parallel to y axis, then the equation of the line is:
x = 2
The line || to x axis has the equation y = d. where d is the distance of the line from x axis.
Since this line y = d has the point (2,-3), y coordinate -3 should satisfy the equation. So -3 = d. Therefore the equation of the line is y = -3. Or y+3 = 0