By comparing the slopes of both lines.
The general form of a straight line is y = mx + c where m is the slope of the line and c is the y-intercept of the line.
For e.g. Consider, the lines y = 2x – 3 and y = 2x – 7.
Now, by comparing these lines with the general form, we get that both of them have slope 2.
Also, by the graph below it can be seen that they both are parallel.
So, it is clear that ‘The slopes of two parallel lines are same’.
Hence, by looking at the standard form of the equation and comparing the slopes, we can determine whether the lines are parallel or not.