# Line Equations in Python

The other day I was playing with some Python challenges found on a popular sites, this challenge worked with xy coordinates on a 2D plane.

I wanted to show some of the code I wrote and how they work.

## The Plane

Being the data is a tuple of x, y coordinates we will use the Cartesian Coordinate System .

I started my code off as a simple Python class:

```
class Line(object):
def __init__(self, data):
self.first, self.second = data
```

Using this Class I can input two points in a tuple like this:

```
data = ((1,1), (2,3))
```

These coordinates would look like this on a 2D plane:

## The Line

The coordinates ((1,1), (2,3)) holds quite a bit of data when it comes to the terms of Algebra.

### Slope

The
Slope
of a line will tell us how steep it is, and can be calculated with the
*change in Y / change int X*
.

```
def slope(self):
'''Get the slope of a line segment'''
(x1, y1), (x2, y2) = self.first, self.second
try:
return (float(y2)-y1)/(float(x2)-x1)
except ZeroDivisionError:
# line is vertical
return None
```

Using the
*slope*
method tells us this line has a slope of
**2**
.

```
>>> data = ((1,1), (2,3))
>>> line = Line(data)
>>> m = line.slope()
>>> print m
2.0
```

### Y Intercept

The
Y Intercept
tells us at what point a line will meet the Y axis. To get a
Y Intercept
we use the equation
*b = y - mx*
where
**m**
is our
*slope*
.

```
def yintercept(self, slope):
'''Get the y intercept of a line segment'''
if slope != None:
x, y = self.first
return y - slope * x
else:
return None
```

And if we plug all our data back in we get a intercept of
**-1**
:

```
>>> b = line.yintercept(slope)
>>> print b
-1.0
```

### Solve for Y

Now that we know the
**slope**
of our line, and where our line meets the
*Y Axis*
we can plug in any
**X**
coordinate and solve for where
**Y**
will be:

```
def solve_for_y(self, x, slope, yintercept):
'''Solve for Y cord using line equation'''
if slope != None and yintercept != None:
return float(slope) * x + float(yintercept)
else:
raise Exception('Can not solve on a vertical line')
```

And just like that we can when
**X**
is equal to
**3**
our
**Y**
will be
**5**
, just look at the graph above and imagaine.

```
>>> line.solve_for_y(3, m, b)
5.0
```

### Solve for X

And lastly using our
**slope**
and
**Y intercept**
we can solve for
**X**
when
**Y**
is some value:

```
def solve_for_x(self, y, slope, yintercept):
'''Solve for X cord using line equatio'''
if slope != 0 and slope:
return float((y - float(yintercept))) / float(slope)
else:
raise Exception('Can not solve on a horizontal line')
```

And we can do the reverse of above to verify they are both working, when
**X**
is equal to
**5**
our
**Y**
should be
**3**
:

```
>>> line.solve_for_x(5, m, b)
3.0
```

## Put it all together

```
class Line(object):
def __init__(self, data):
self.first, self.second = data
def slope(self):
'''Get the slope of a line segment'''
(x1, y1), (x2, y2) = self.first, self.second
try:
return (float(y2)-y1)/(float(x2)-x1)
except ZeroDivisionError:
# line is vertical
return None
def yintercept(self, slope):
'''Get the y intercept of a line segment'''
if slope != None:
x, y = self.first
return y - slope * x
else:
return None
def solve_for_y(self, x, slope, yintercept):
'''Solve for Y cord using line equation'''
if slope != None and yintercept != None:
return float(slope) * x + float(yintercept)
else:
raise Exception('Can not solve on a vertical line')
def solve_for_x(self, y, slope, yintercept):
'''Solve for X cord using line equatio'''
if slope != 0 and slope:
return float((y - float(yintercept))) / float(slope)
else:
raise Exception('Can not solve on a horizontal line')
```