Thread: Equations of the line

I have a query, if I have two equations i.e. y = 6x + 3 and say y = 6x - 3 and was asked to advise if they intersected, would you put any previous values given into the above like x- = -4 as an example, or would you leave them in their original form and answer the query as they are given without values.

My solutions show that whether values are put in or not they are parrallel lines and don't intersect, anyone like to comment?

Cheers

David

Originally Posted by David Green

I have a query, if I have two equations i.e. y = 6x + 3 and say y = 6x - 3 and was asked to advise if they intersected, would you put any previous values given into the above like x- = -4 as an example, or would you leave them in their original form and answer the query as they are given without values.

My solutions show that whether values are put in or not they are parrallel lines and don't intersect, anyone like to comment?

Cheers

David

No, you don't need to substitute values. Like you said, it's clear from the two lines having the same gradient that they are parallel, and therefore they never intersect.

Putting in, say, x= -4, and showing that you get different y values only shows that they don't intersect at x= -4 but might intersect elsewhere. As Prove It said, the simplest thing to do is just to observe that both lines have the same gradient (I would say "slope"). However, another way to show they do not intersect is to try to find a point of intersection. If (x,y) lies on both lines, then we must have y= 6x+ 3= 6x- 3 which reduces to the equation 3= -3 which is false no matter what x is.

(It just occured to me. Just having the same slope (gradient) does NOT necessarily mean that two lines do not intersect! They might be the same line. y= 6x+ 3 and 2y= 12x+ 6 have the same slope but if we set y= y, we get 12x+ 6= 12x+ 6 which is true for all x. Those two equations give the same line.)