SOLUTION: How do you write an equation of the line containing the given point and parallel to (2,-1) 6x-7y=8. How do you find what y is equal to?

Algebra ->  Linear-equations -> SOLUTION: How do you write an equation of the line containing the given point and parallel to (2,-1) 6x-7y=8. How do you find what y is equal to?      Log On


   

Question 1090924: How do you write an equation of the line containing the given point and parallel to (2,-1) 6x-7y=8. How do you find what y is equal to?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
an equation of the line containing the given point (2,-1)
and parallel to
6x-7y=8
6x-8=7y
y=%286%2F7%29x-8%2F7

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 6%2F7 (its from the slope of y=%286%2F7%29%2Ax%2B8%2F7 which is also 6%2F7). Also since the unknown line goes through (2,-1), 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%2B1=%286%2F7%29%2A%28x-2%29 Plug in m=6%2F7, x%5B1%5D=2, and y%5B1%5D=-1



y%2B1=%286%2F7%29%2Ax-%286%2F7%29%282%29 Distribute 6%2F7



y%2B1=%286%2F7%29%2Ax-12%2F7 Multiply



y=%286%2F7%29%2Ax-12%2F7-1Subtract -1 from both sides to isolate y

y=%286%2F7%29%2Ax-12%2F7-7%2F7 Make into equivalent fractions with equal denominators



y=%286%2F7%29%2Ax-19%2F7 Combine the fractions



y=%286%2F7%29%2Ax-19%2F7 Reduce any fractions

So the equation of the line that is parallel to y=%286%2F7%29%2Ax%2B8%2F7 and goes through (2,-1) is y=%286%2F7%29%2Ax-19%2F7


So here are the graphs of the equations y=%286%2F7%29%2Ax%2B8%2F7 and y=%286%2F7%29%2Ax-19%2F7



graph of the given equation y=%286%2F7%29%2Ax%2B8%2F7 (red) and graph of the line y=%286%2F7%29%2Ax-19%2F7(green) that is parallel to the given graph and goes through (2,-1)