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Question
Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
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Solution
It can be observed that point (2, 14) satisfies the equation 7x − y = 0 and
x − y + 12 = 0.
Therefore, 7x − y = 0 and x − y + 12 = 0 are two lines passing through point (2, 14).
As it is known that through one point, infinite number of lines can pass through, therefore, there are infinite lines of such type passing through the given point.
It can be observed that point (2, 14) satisfies the equation 7x − y = 0 and
x − y + 12 = 0.
Therefore, 7x − y = 0 and x − y + 12 = 0 are two lines passing through point (2, 14).
As it is known that through one point, infinite number of lines can pass through, therefore, there are infinite lines of such type passing through the given point.
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