SOLUTION: I need to write an equation of a line containing point (4,-9) and parrellel to the line 6x-5y=7

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Question 121730: I need to write an equation of a line containing point (4,-9) and parrellel to the line 6x-5y=7
Found 2 solutions by checkley71, MathLover1:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST WE NEED TO FIND THE SLOPE OF THIS EQUATION.
6X-5Y=7
-5Y=-6X+7
Y=-6X/-5+7/-5
Y=6X/5-7/5 ( RED LINE) HERE THE SLOPE=6/5.
NOW REPLACE X & Y BY 4 & -9 ALONG WITH THE SLOPE=6/5 & SOLVE FOR THE Y INTERCEPT(b) IN THE LINE FORMULA [Y=mX+b]
-9=6/5*4+b
-9=24/5+b
b=-9-24/5
b=(-9*5-24)/5
b=(-45-24)/5
b=-69/5 OR
Y=6X/5-69/5 (GREEN LINE)
+graph%28+300%2C+300%2C+-6%2C+20%2C+-15%2C+15%2C+y+=+6x%2F5+-7%2F5%2C+y+=+6x%2F5+-69%2F5%29+ (graph 300x300 pixels, x from -6 to 20, y from -15 to 15, of TWO functions y = 6x/5 -7/5 and y = 6x/5 -69/5).

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 1.2 (its from the slope of y=1.2%2Ax-1.4 which is also 1.2). Also since the unknown line goes through (4,-9), 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%2B9=1.2%2A%28x-4%29 Plug in m=1.2, x%5B1%5D=4, and y%5B1%5D=-9



y%2B9=1.2%2Ax-%281.2%29%284%29 Distribute 1.2



y%2B9=1.2%2Ax-4.8 Multiply



y=1.2%2Ax-4.8-9Subtract -9 from both sides to isolate y

y=1.2%2Ax-13.8 Combine like terms

So the equation of the line that is parallel to y=1.2%2Ax-1.4 and goes through (4,-9) is y=1.2%2Ax-13.8


So here are the graphs of the equations y=1.2%2Ax-1.4 and y=1.2%2Ax-13.8



graph of the given equation y=1.2%2Ax-1.4 (red) and graph of the line y=1.2%2Ax-13.8(green) that is parallel to the given graph and goes through (4,-9)