A line has the equation #2y=-3x+1#, how do you find an equation of a line parallel to this line that has a y intercept of -2?

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1 Answer
smendyka
Jan 10, 2017

See the process for solving this problem below in the Explanation:

Explanation:

First, we need to put the line from the problem in the slope-intercept form by solving for #y#:

#(2y)/color(red)(2) = (-3x + 1)/color(red)(2)#

#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = -3/2x + 1/2#

#y = -3/2x + 1/2#

The slope-intercept form of a linear equation is:

#y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b# is the y-intercept value.

So we know the slope of the line from the question is #-3/2#

And, a parallel line by definition has the same slope so the slope of the line we are looking for also has a slope of #-3/2#

And because we know the #y# intercept, #-2#, we can substitute both these values into the slope-intercept formula to find the equation we are looking for:

#y = color(red)(-3/2)x + color(blue)(-2)#

#y = color(red)(-3/2)x - color(blue)(2)#

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