SOLUTION: Consider the line y= -7x+8. Find the equation of the line that is parallel to this line and passes through the point(5,9). Find the equation of the line that is perpendicula

Algebra ->  Graphs -> SOLUTION: Consider the line y= -7x+8. Find the equation of the line that is parallel to this line and passes through the point(5,9). Find the equation of the line that is perpendicula      Log On


   

Question 98404: Consider the line y= -7x+8.

Find the equation of the line that is parallel to this line and passes through the point(5,9).
Find the equation of the line that is perpendicular to this line and passes through the point(5.9) .

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=-7X+8 (RED LINE) HAS A SLOPE OF -7.
THUS A PARALLEL LINE THROUGH (5,9) WITH A SLOPE OF -7 IS:
9=-7*5+b
9=-35+b
b=9+35
b=44 FOR THE Y INTERCEPT.
THUS THIS LINE EQUATION IS:
Y=-7X+44 (GREEN LINE)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+50%2C+y+=+-7x+%2B8%2C+y+=+-7x+%2B44%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 50, of TWO functions y = -7x +8 and y = -7x +44).
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A PERPENDICULAR LINE WILL HAVE A SLOPE OF 1/7 (THE NEGATIVE RECIPRICAL OF -7)
9=5/7+b
9-5/7=b
b=(63-5)/7
b=58/7 FOR THIS Y INTERCEPT.
Y=X/7+58/7 IS THIS LINE EQUATION (GREEN LINE)
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+y+=+-7x+%2B8%2C+y+=+x%2F7+%2B58%2F7%29+ (graph 300x200 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = -7x +8 and y = x/7 +58/7).