# data[].attributes.body
in parallel lines, the gradient of the lines must be the same.
for example:
y = -1.5x + 3
y = -1.5x -2

# data[].attributes.body
To lines are parallel when their equations have the same gradient. For example:
y=2x+1
y=2x-34
And for two lines to be perpendicular, their gradients have to be opposites and reciprocals.
For example:
y=4x-2
y=-1/4x-45

# data[].attributes.body
Lines that are parallel must have the same gradient

# data[].attributes.body
there are two different ways to calculate the equation of the straight line:
- y= mx + n
- ax+by+c=0

# data[].attributes.body
in the equation
ax+by+c = 0
all the numbers must be integer numbers.

# data[].attributes.headline
VICKY: find the equation of  the gradient and a point on the line 

# data[].attributes.subject
VICKY: find the equation of  the gradient and a point on the line 

# data[].attributes.body
example:
We know that the line has equation y=mx+cy=mx+c, and we know that m=3m=3, so the equation is y=3x+cy=3x+c.

Now when x=1x=1, we must have y=2y=2, as the point (1,2)(1,2) lies on the line.

So we can substitute in x=1 and y=2 to get.
2= 3 . 1 + c
2= 3+ c
c= -1

# data[].attributes.body
for two lines to be parallel they need to have the same gradient (m)

# data[].attributes.body
for two lines to be perpendicular their gradient has to be the opposite and reciprocals

# data[].attributes.body
To calculate m you use the following equation:
y2 - y1
-----------
x2 - x1

# data[].attributes.body
a line that goes straight across has a gradient of 0

# data[].attributes.body
a line is perpendicular to another one when its gradient is reciprocal and opposite.
For example: y=4/3x+1
y=-3/4-8

# data[].attributes.body
to calculate n you have to take the coordinates of one of the points of the line and then replace the y and the x