Segment AB is on the line y − 4 = −5(x − 1), and segment CD is on the line y − 4 = one fifth(x − 5). Which statement proves the relationship of segments AB and CD? They are perpendicular because they have slopes that are opposite reciprocals of 5 and negative one fifth.
They are perpendicular because they have slopes that are opposite reciprocals of −5 and one fifth.
They are parallel because they have the same slope of 5.
They are parallel because they have the same slope of negative one fifth

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step-by-step explanation:

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9