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Line 1: m = 2

Line 2: m = 2

The lines are parallel.

Step-by-step explanation:

First, ensure both lines are in the slope-intercept form given as y = mx + b. where m is the slope of the line.

If the slope of both lines are the same, they are parallel.

If the slope of one is the negative reciprocal of the other, they are perpendicular.

If the slope of both lines are different and one is neither the reciprocal of the other, then they are neither parallel nor perpendicular.

✍️Line 1, y = 2x + 5, is already in the slope-intercept form.

✅The slope of Line 1 is 2

✍️Line 2, y - 3 = 2(x + 15), is in point-slope.

We can decide to rewrite in the slope-intercept form or directly determine the slope as it is given. The slope is 2. But to be sure, let's rewrite as y = mx + b.

y - 3 = 2(x + 15)

y - 3 = 2x + 30

Add 3 to both sides

y = 2x + 33

✅As we can see, the slope of line 2 is 2.

✍️Line 1 and line 2 has the same slope of 2, therefore the lines are parallel.

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