# find the equation of the straight line which passes through (2,-3) and is parallel with x axis or is parallel with y axis.

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### 3 Answers

We have 2 cases:

Case (1):

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

Case 2:

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