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Determine wether the graphs of the pair of lines are parallel4x - y = 163y - 12x = - 3

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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

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