# Determine whether the graphs pf the twp equations are perpendicular.?

y=9x-2

6y=5-x

are the graphs of the given equations perpendicular?

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In order to know whether the two lines are in perpendicular, you need to focus on their gradient.

Let m1 be the gradient of linear equation 1, y=(m1)x+c

and m2 be the gradient of liners equation 2, y=(m2)x+c

then if m1 times m2 equal to -1, then the two lines are perpendicular.

For example, if m1 is 2, then m2 need to be (-1/2) in order to form perpendicular with line 1.

So, take your question as an example.

Write both of them in the form of y=mx+c

Linear Equation 1 : y=9x-2 ; hence, m1=9

Linear Equation 2 : 6y=5-x

y=(-1/6)x+(5/6) ; hence m2=(-1/6)

Since m1*m2 is not equal to -1, [ which is 9*(-1/6)=(-3/2) ],

so, the two liners equation given are not in perpendicular.

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• Perpendicular means the slopes are opposite reciprocals. You need to find the slope of each line to see

y = 9x - 2 m = 9/1

y = (-1/6)x + 5/6 m = -1/6

NOT perpendicular! the slope of the second line wouldn't needed to be m = -1/9

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• To be perpendicular, the slopes must be the unfavourable reciprocal 5x -2y = 7, 5y - 2x = 3 2y=5x-7 or y = 5/2 x-7/2 5y = 2x+3 or y =2/5 x+3/5 is reciprocal yet no longer unfavourable, so no is the respond

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• Not perpendicular.

Because m1m2 does not equal to -1

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