A line passes through #(5 ,8 )# and #(6 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
(2 ,-3)
There are 2 approaches we can take for this question.
(1) Using definition of gradient.
(2) Using equation of line passing through (1 ,3)
Method 1 Using the gradient
Thus from (1 ,3) → (1+1 ,3-6) → (2 ,-3) is a point on line.
or we could move 1 left and 6 up (equivalent to subtracting 1 from x-coord and adding 6 to y-coord)
Thus from (1 ,3) → (1-1 ,3+6) → (0 ,9) is another point on the line.
Method 2 Using equation of line
We know m = -6 hence partial equation is y = -6x +b
Using (1 ,3) to find b → 3 = -6 + b → b = 9
Choosing any value for x and substituting into equation to find corresponding y-coordinate.
x = 0 : y = 0 + 9 = 9 → (0 ,9) is a point on line
x = 2 : y = -12 + 9 = -3 → (2 ,-3) is another point on the line
These are the same points generated using Method 1 above
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One other point that the second line may pass through if it is parallel to the first line is (2, -1).
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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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