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)?
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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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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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