Find the equation of line perpendicular to #y=-5/3x-8# and passing through #(-9,-3)#?

Answer 1

#3x-5y+12=0#

The two lines are perpendicular to each other, if the product of their slopes is #-1#. Hence if slope of one line is given as #a/b#, slope of line perpendicular to it is #-b/a#.
As equation of one line is given in slope-intercept form as #y=-5/3x-8#, its slope is #-5/3#.
Hence slope of line perpendicular to it is #3/5#.
Now equation of line passing through #(x_1,y_1)# and having slope #m# is #(y-y_1)=m(x-x_1)#
Hence, equation of a line passing through #(-9,-3)# and having a slope #3/5# is
#(y-(-3))=3/5(x-(-9))#
or #5(y+3)=3(x+9)#
or #5y+15=3x+27#
or #3x-5y+12=0# graph{(3x-5y+12)(y+5x/3+8)((x+9)^2+(y+3)^2-0.05)=0 [-20, 20, -10, 10]}
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Answer 2

First, find the slope of the given line. Then, determine the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, use the point-slope form of the equation of a line, (y - y_1 = m(x - x_1)), where (m) is the slope and ((x_1, y_1)) is the given point, to find the equation of the perpendicular line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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