Parallel lines have the same gradient.
From this, we get one of the two following cases:
Two parallel lines that never cross and don't have any points in common. 
Two parallel lines that are identical and share all points in common. 
Let's look at how we can identify parallel lines given their equations.
Equation Form  Characteristic of parallel lines  Examples 

$y=mx+b$y=mx+b  Parallel lines have the same $m$m value. 
$y=2x1$y=2x−1 $y=4+2x$y=4+2x 
$ax+by+c=0$ax+by+c=0  Parallel lines have the same value of $\frac{a}{b}$−ab. 
$x+2y3=0$x+2y−3=0 $2x+4y+1=0$2x+4y+1=0 
For every straight line $y=mx+b$y=mx+b, there exist infinitely many lines parallel to it.


Is the line $y=4x1$y=4x−1 parallel to $y=4x6$y=4x−6 ?
Yes
No
If the line formed by equation $1$1 is parallel to the line formed by equation $2$2, fill in the missing value below.
Equation $1$1: $y$y$=$= $\editable{}$ $x$x$+$+$4$4
Equation $2$2: $y$y$=$=$\frac{4}{5}x$45x$$−$7$7
Consider the following points on the number plane:
$A$A $\left(1,4\right)$(1,−4)
$B$B $\left(2,8\right)$(−2,8)
$C$C $\left(5,2\right)$(−5,2)
$D$D $\left(1,22\right)$(1,−22)
First, calculate the gradient of the line $AB$AB.
Now, find the gradient of the line $CD$CD.
Is the line $CD$CD parallel to $AB$AB?
Yes
No
Assess whether the points $A$A, $B$B and $C$C are collinear.
If $A$A and $B$B have the coordinates $\left(0,2\right)$(0,2) and $\left(5,27\right)$(5,27) respectively, evaluate the gradient of the line $AB$AB.
If $C$C has the coordinates $\left(1,7\right)$(1,7), evaluate the gradient of the line $BC$BC.
Based on these two gradients, are $A$A, $B$B and $C$C collinear?
Yes
No