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Question 160254: Write an equation of the line containing the given point and parallel to the given line.
(8,-2); 6x-7y=2
The equation of the line is y=__________
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! Write an equation of the line containing the given point and parallel to the given line.
(8,-2); 6x-7y=2
The equation of the line is y=__________
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the equation for the given line is 6*x - 7*y = 2
convert this to slope intercept form of the equation which is y = m*x + b
subtracting 6*x from both side of the equation gets -7*y = -6*x - 2
dividing both sides of the equation by (-7) gets y = (-6/-7)*x - (2/-7)
which becomes y = (6/7)*x - (2/7)
the slope of the line is (6/7) and the y intercept is -(2/7).
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you want a line with the same slope (parallel lines have the same slope) intersecting with the point (8,-2)
the slope intercept form of the equation going through the point (x1,y1) would be y = m*(x-x1) + y1
since (x1,y1) = (8,-2), then
x1 = 8
y1 = (-2)
since the slope is the same as the given line,
m = (6/7)
slope intercept form then becomes y = (6/7)*(x - 8) + (-2)
this becomes y = (6/7)*x - 8*(6/7) + (-2)
this becomes y = (6/7)*x - 48/7 - 14/7
this becomes y = (6/7)*x - (48+14)/7
this becomes y = (6/7)*x - (62/7)
to prove this equation is correct, substitute for x and y in the equation
y = (6/7)*x - (62/7) using the point (8,-2).
equation then becomes
-2 = (6/7)*8) - (62/7)
which becomes
-2 = 48/7 - (62/7)
which becomes
-2 = (48-62)/7
which becomes
-2 = -14/7
which becomes
-2 = -2
equation is good.
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slope intercept form of the equation is y = (6/7)*x - (62/7)
standard form of the equation would be a*x + b*y = c
to convert the slope intercept form to the standard form do the following:
y = (6/7)*x - (62/7)
multiply both sides by 7 to remove the denominators.
7*y = 6*x - 62
add 62 to both sides of the equation and subtract 7*y from both sides of the equation
62 = 6*x - 7*y
this is the same as 6*x - 7*y = 62 which is the standard form of the equation.
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a graph of both equations will look like this
please scan below the graph for additional comments
the lines are parallel and the graph of (6/7)*x - (62/7) intersects with the point (8,-2).
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