SOLUTION: Use the given conditions to write an equation for the line in point-slope form. Passing through  (−5,5) 

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Question 950382:
Use the given conditions to write an equation for the line in point-slope form.
Passing through 
(−5,5) 
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

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 5%2F6 (its from the slope of y=%285%2F6%29%2Ax%2B1%2F6 which is also 5%2F6). Also since the unknown line goes through (-5,5), 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-5=%285%2F6%29%2A%28x%2B5%29 Plug in m=5%2F6, x%5B1%5D=-5, and y%5B1%5D=5



y-5=%285%2F6%29%2Ax-%285%2F6%29%28-5%29 Distribute 5%2F6



y-5=%285%2F6%29%2Ax%2B25%2F6 Multiply



y=%285%2F6%29%2Ax%2B25%2F6%2B5Add 5 to both sides to isolate y

y=%285%2F6%29%2Ax%2B25%2F6%2B30%2F6 Make into equivalent fractions with equal denominators



y=%285%2F6%29%2Ax%2B55%2F6 Combine the fractions



y=%285%2F6%29%2Ax%2B55%2F6 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F6%29%2Ax%2B1%2F6 and goes through (-5,5) is y=%285%2F6%29%2Ax%2B55%2F6


So here are the graphs of the equations y=%285%2F6%29%2Ax%2B1%2F6 and y=%285%2F6%29%2Ax%2B55%2F6



graph of the given equation y=%285%2F6%29%2Ax%2B1%2F6 (red) and graph of the line y=%285%2F6%29%2Ax%2B55%2F6(green) that is parallel to the given graph and goes through (-5,5)