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Question 884246: I've tried so many things to be solving equations like this. I've asked adults, friends, siblings and neighbors and no one seems to know. Please help! and the problem is :"Please write the equations of the following lines:"
a) contains (6,-1) and parallel y=2/7x+3
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the line contains the point (6,-1) and is parallel to y = (2/7)x + 3
if the line is parallel to y = (2/7)x + 3 then it has the same slope.
the equation of the line is in the slope intercept form of y = mx + b where m is the slope and b is the y intercept.
the slope of the line is (2/7) so the slope of your new line also has to be (2/7).
start with y = (2/7)x + b
since the point (6,-1) is on the line, you can replace y with -1 and x with 6 to get:
-1 = (2/7)*6 + b
now you want to solve for b.
simplify to get:
-1 = 12/7 + b
subtract 12/7 from both sides of the equation to get:
-1 - 12/7 = b
since -1 is the same as -7/7, your equation becomes:
-7/7 - 12/7 = b
combine the fractions with the same denominator to get:
-17/7 = b
your new equation is y = (2/7)x - 17/7
once you know the slope, you can also solve for the equation by using the point slope form of the equation of a straight line.
that form is y-y1 = m(x-x1)
m is equal to (2/7)
y1 is equal to -1
x is equal to 6
you get:
y + 1 = (2/7)(x-6)
simplify to get:
y + 1 = (2/7)x - 12/7
subtract 1 from both sides of the equation to get:
y = (2/7)x - 12/7 - 1
since -1 is equivalent to -7/7, you get:
y = (2/7)x - 12/7 - 7/7 which results in:
y = (2/7)x - 17/7
that's your equation.
a graph of your equation and the original equation of y = (2/7)x + 3 is shown below:
as you can see, the lines are parallel and the bottom line goes through the point (6,-1).
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