What is the equation of the line perpendicular to #y=-2/21x # that passes through # (-1,6) #?

Answer 1

The slope of a perpendicular line is the negative reciprocal of the original line.

The slope of the perpendicular line is #21/2#, since the original line has a slope of #-2/21#.

Now that we have the point, the slope abs can be used to find the slope intercept form equation using point slope form.

#y - y_1 = m(x - x_1)#
The point (-1,6) is #(x_1, y_1)# while m is the slope.
#y - 6 = 21/2(x - (-1))#
#y - 6 = 21/2x + 21/2#
#y = 21/2x + 21/2 + 6#
#y = 21/2x + 33/2#

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Answer 2

#y=21/2x+33/2#

Given:#" "y=-2/21x# ..............................(1)

Compare to the standard form of#" " y= mx+c#

Where
#m# is the gradient
#x# is the independent variable (can take any value you wish)
#y# is the dependant variable. Its value depend on that of #x#
#c# is a constant that for a straight line graph is the y-intercept

In your equation #c=0# the #"y-intercept "-> y=0#

If #m# is the gradient of the given line then #-1/m# is the gradient of a line perpendicular to it.

#color(blue)("So for the perpendicular line")#

#" "y_("perp") = (-1)xx(-21/2)xx x + c#

#color(blue)(" "y_("perp") = +21/2x + c)#......................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the value of "c)#

We know that this new line passes through#(x,y)->(-1,6)#

So substitute into equation (2) the values #(x,y)->(color(green)(-1),color(magenta)(6))#

#" "y_("perp") =color(magenta)(6) = +21/2(color(green)(-1)) + c......................(2_a)#

#color(blue)(c=6+21/2 = 33/2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

The line perpendicular to that given is: #y=21/2x+33/2#

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Answer 3

To find the equation of the line perpendicular to ( y = -\frac{2}{21}x ), first, determine the slope of the given line. Then, find the negative reciprocal of that slope to obtain the slope of the perpendicular line. Next, use the point-slope form of the equation of a line, substituting the slope and the given point ((-1, 6)) into the equation. Finally, simplify the equation to put it in slope-intercept form, if necessary.

  1. Slope of the given line: ( m = -\frac{2}{21} )
  2. Slope of the perpendicular line: ( m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{-\frac{2}{21}} = \frac{21}{2} )
  3. Using the point-slope form with the given point ((-1, 6)): [ y - y_1 = m(x - x_1) ] [ y - 6 = \frac{21}{2}(x + 1) ]
  4. Simplify the equation: [ y - 6 = \frac{21}{2}x + \frac{21}{2} ] [ y = \frac{21}{2}x + \frac{21}{2} + 6 ] [ y = \frac{21}{2}x + \frac{33}{2} ]
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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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