Two parallel lines have equal slopes. To find the slopes
of the 2 lines, we have to put the equation of the lines in the standard form, which
is:
y = mx + n, where m represents the slope and n is the y
intercept.
We know, from enunciation, that the equation of
one of the 2 lines is y = -2. From this equation, we conclude that the y intercept is
-2, meaning that n = -2 and the slope is m = 0.
According
to the rule, the slopes of 2 parallel lines are equal, we conclude that the slope of the
other line is also m = 0.
We know that the line is passes
through the point (3,4).
That means that the coordinates of
the point verifies the equation of the line: y = mx+n.
4 =
0*3 + n (we've put the slope m = 0)
n =
4
So, the equation of the line, which is parallel to the
line y = -2 and it passes through the point (3,4)
is:
y =
4
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