Question 157835
Hi, Hope I can help,
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Write an equation of the line that is parallel to {{{ y= 3x-4 }}} and passes through point (0,-3). 
PLEASE HELP- Thanks!
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You are trying to find a parallel line to {{{ y = 3x - 4 }}}, which means the line has the same slope
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the slope intercept form of a line = {{{ y = mx+b }}}, ( "m" = slope )("b" = y intercept)
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Since we know the slope of both lines ( slope = 3)(parallel lines have same slope), We can replace "m" with "3" in our equation
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{{{ y = mx+b }}} = {{{ y = (3)x+b }}} = {{{ y = 3x+b }}}
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Since the line includes the point (0,-3), points are given as (x,y), we can replace "x" and "y" with the numbers( replace "x" with "0", "y" with (-3) )
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{{{ y = 3x+b }}} = {{{ (-3) = 3(0)+b }}} = {{{ (-3) = 0+b }}} = {{{ (-3) = b }}}
= {{{ b = (-3) }}}
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We can replace "b" with (-3) in our equation
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{{{ y = 3x+b }}} = {{{ y = 3x+(-3) }}} = {{{ y = 3x-3 }}}
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You can check our equation by replacing "x" and "y" again, with (0,-3)(x,y) in our equation
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{{{ y = 3x-3 }}} = {{{ (-3) = 3(0)-3 }}} = {{{ (-3) = 0-3 }}} = {{{ (-3) = (-3) }}} (True)
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{{{ y = 3x-3 }}} is your answer,
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Here are the graphs of the two lines
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green line = {{{ y = 3x-4 }}}
red/brown line = {{{ y = 3x-3 }}}
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{{{ drawing (600,600,-10,10,-10,10,grid(1),graph(600,600,-10,10,-10,10,3x-3,3x-4)) }}}
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As you can see, line {{{ y = 3x-3 }}} is parallel to {{{ y = 3x-4 }}}
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{{{ y = 3x-3 }}} is your answer
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Hope I helped, Levi