Determine if the equations represent lines that are parallel, perpendicular, or neither.

lines are parallel and m = 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

14x = 2y - 6 or

2y - 6 = 14x ( add 6 to both sides )

2y = 14x + 6 ( divide through by 2 )

y = 7x + 3 ← in slope- intercept form

with slope m = 7

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= y - 7x or

y - 7x = ( add 7x to both sides )

y = 7x + ← in slope- intercept form

with slope m = 7

Since slopes of both lines are equal, both m = 7 then lines are parallel

Congruent

Step-by-step explanation:

The alternate interior angle theorem states that if two lines are parallel and are interesected by a line, the alternate angles on either side of the interior of the line are congruent. Angles two and three, in the interior, which are not shown, are also congruent and are both supplementary to 1 and 4.