The first step is to determine the slope of both lines. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents the slope
c represents y intercept
The given equations are
4x - y = 16
3y - 12x = - 3
We would rewrite each equation so that it would take the form of the slope intercept equation.
For 4x - y = 16,
Adding y to both sides of the equation, we have
4x - y + y = 16 + y
4x = 16 + y
subtracting 16 from both sides of the equation, we have
4x - 16 = 16 - 16 + y
4x - 16 = y
y = 4x - 16
Thus, slope = 4
For 3y - 12x = - 3,
We would add 12x to both sides of the equation. It becomes
3y - 12x + 12x = 12x - 3
3y = 12x - 3
Dividing both sides of the equation by 3, we have
3y/3 = 12x/3 - 3/3
y = 4x - 1
Thus, slope = 4
Recall, if two lines are parallel, it means that they have the same slope. Since the slopes of the given lines are equal, then
They are parallel