SOLUTION: Find equation of the line that passes through points (-3,8) and is parallel to 2x-6y=7

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Question 120512: Find equation of the line that passes through points (-3,8) and is parallel to 2x-6y=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



First convert the standard equation 2x-6y=7 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


2x-6y=7 Start with the given equation


2x-6y-2x=7-2x Subtract 2x from both sides


-6y=-2x%2B7 Simplify


%28-6y%29%2F%28-6%29=%28-2x%2B7%29%2F%28-6%29 Divide both sides by -6 to isolate y


y+=+%28-2x%29%2F%28-6%29%2B%287%29%2F%28-6%29 Break up the fraction on the right hand side


y+=+%281%2F3%29x-7%2F6 Reduce and simplify


The original equation 2x-6y=7 (standard form) is equivalent to y+=+%281%2F3%29x-7%2F6 (slope-intercept form)


The equation y+=+%281%2F3%29x-7%2F6 is in the form y=mx%2Bb where m=1%2F3 is the slope and b=-7%2F6 is the y intercept.








Now let's find the equation of the line that is parallel to y=%281%2F3%29x-7%2F6 which goes through (-3,8)

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1%2F3 (its from the slope of y=%281%2F3%29%2Ax-7%2F6 which is also 1%2F3). Also since the unknown line goes through (-3,8), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-8=%281%2F3%29%2A%28x%2B3%29 Plug in m=1%2F3, x%5B1%5D=-3, and y%5B1%5D=8



y-8=%281%2F3%29%2Ax-%281%2F3%29%28-3%29 Distribute 1%2F3



y-8=%281%2F3%29%2Ax%2B3%2F3 Multiply



y=%281%2F3%29%2Ax%2B3%2F3%2B8Add 8 to both sides to isolate y

y=%281%2F3%29%2Ax%2B3%2F3%2B24%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B27%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B9 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F3%29%2Ax-7%2F6 and goes through (-3,8) is y=%281%2F3%29%2Ax%2B9


So here are the graphs of the equations y=%281%2F3%29%2Ax-7%2F6 and y=%281%2F3%29%2Ax%2B9



graph of the given equation y=%281%2F3%29%2Ax-7%2F6 (red) and graph of the line y=%281%2F3%29%2Ax%2B9(green) that is parallel to the given graph and goes through (-3,8)