Question

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Answer 1

Hint: To form equations we can use different possibilities with x and y which means we can try to form equations with the points.

Complete step-by-step answer:

Since, the given solution is (2, 14).

Therefore the x-coordinate = 2 and,

The y-coordinate = 14

Then, one of the equations can be $x + y = 2 + 14 = 16$

Therefore, $x + y = 16$

Similarly, the second equation can be $x - y = 2 - 14 = - 12$

Therefore, $x - y = - 12$

And, the third equation can be $y = 7x$

Therefore, $7x - y = 0$.

Similarly, another equation can be$ - x + y = - 2 + 14 = 12$.

Therefore, $ - x + y = 12$

Similarly, another equation can be$ - 2x - y = - 2(2) - 14 = 18$.

Therefore, $ - 2x - y = 18$

So, we can find infinite equations for the given point passing through it.

So, from the above figure, if we consider the point as P, we can draw an infinite number of lines passing through the point.

Note: Consider a point in a plane and pass a line through it and we can pass many lines coming from different directions and there is no end to it. The properties of a point also state that infinite lines can pass through the given point.