What is the equation of the line that passes through #(-2,1) # and is perpendicular to the line that passes through the following points: #(-3,6),(7,-3)?

Answer 1

#9y-10x-29=0#

Gradient of #(-3,6)# and #(7,-3)# #m_1=(6--3)/(-3-7)=9/-10#
For perpendicular lines, #m_1m_2=-1# so #m_2=10/9#
Using the point gradient formula, #(y-1)=10/9(x+2)#
#9y-9=10x+20#
#9y-10x-29=0#
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Answer 2

First, let's find the slope of the line passing through the points (-3,6) and (7,-3).

Slope (m) = (\frac{y_2 - y_1}{x_2 - x_1})

(m = \frac{-3 - 6}{7 - (-3)})

(m = \frac{-9}{10})

The line perpendicular to this line will have a slope that is the negative reciprocal of (\frac{-9}{10}), which is (\frac{10}{9}).

Now, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (-2,1) with slope (\frac{10}{9}).

(y - y_1 = m(x - x_1))

(y - 1 = \frac{10}{9}(x + 2))

(y - 1 = \frac{10}{9}x + \frac{20}{9})

(y = \frac{10}{9}x + \frac{20}{9} + 1)

(y = \frac{10}{9}x + \frac{20}{9} + \frac{9}{9})

(y = \frac{10}{9}x + \frac{29}{9})

So, the equation of the line that passes through (-2,1) and is perpendicular to the line passing through (-3,6) and (7,-3) is (y = \frac{10}{9}x + \frac{29}{9}).

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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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