What is the equation of the line the passes through the point #(0, 2)# and is parallel to #6y=5x-24#?

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Answer 1 · 2016-11-15T11:25:52

The equation of the line passing through #(0,2)# is # 6y=5x+12#.

Parallel lines have equal slopes.
The slope of the line #6y=5x-24 or y= 5/6*x-4# is #5/6#

So the slope of the line passing through #(0,2)# is also #5/6#

The equation of the line passing through #(0,2)# is #y-2=5/6*(x-0) or y-2 = 5/6 x or 6y-12=5x or 6y=5x+12# [Ans]

Answer 2 · 2016-11-15T12:48:11

#y = 5/6x +2#

The first thing you should notice is that the point #color(red)((0,2)#
is a specific point on the line.

The #x# value = 0, tells us that the point is on the y-axis.

In fact it is #c " "rarr# the y-intercept.

Parallel lines have the same slope.

#6y = 5x-24# can be changed to

#y = color(blue)(5/6)x -4" "larr m = color(blue)(5/6)#

The equation of a line can be written in the form #y =color(blue)(m)x + color(red)(c)#

We have both m and c, substitute them into the equation.

#y =color(blue)(5/6)x + color(red)(2)#