Jump to content

Math


Georgiy

Recommended Posts

  • 3 weeks later...

Your question is simply too vague.  Find the equation of a line given what information?  Most common is "find the equation of the line through two given points".  But you could also be asked to "find the equation of the line through a given point having a given slope" or "find the equation othf the line through a given point parallel to a given line" or "find the equation of the line through a given point perpendicular to a given line".  

Any (non-vertical) line can be written "y= ax+ b".  If you are given two points you can put the x, y coordinates into that equation to get two equations to solve for a and b.  For example, if the two points are (3, 5) and (7, 9) then we have 5= 3a+ b and 9= 7a+ b.  Subtracting the first equation from the second, 4= 4a so a= 1.  Then 5= 3+ b so b= 5- 3= 2.  The line is given by y= x+ 2.  

If you are given the point (3, 5) and slope 3 then, because the "a" in "y= ax+ b" is the slope, a= 3.  Putting the x= 3, y= 5 in y= 3x+ b we have 5= 3(3)+ b so b= 5- 9= -4.  The line is given by y= 3x- 4.

If you are given the point (3, 5) and are told that the line is parallel to the line y= 7x+ 9 then the slope is the same as the slope of the given line, 7, so we have the previous problem: 5= 7(3)+ b.  b= 5- 21= -16.  The line is given by y= 7x- 16.

If you are given the point (3, 6) and are told that the line is perpendicular to the line y= 4x- 5 then the slope is the negative reciprocal of the slope of the given line, -1/4, so we gave 6= (-1/4)(3)+ b.  b= 6+ 3/4= 27/4.  The line is given by y= (-1/4)x+ 27/4.  We can also write that as 4y= 27- x or x+ 4y= 27.

(Any vertical line can be written x= constant.  The x-value of a given point on the line gives you the constant.)

Edited by Country Boy
Link to comment
Share on other sites

  • 1 month later...

Well, first of all, we need to know is it a straight line? then, as druS mentioned, we may use the equation y = mx + c for a straight line.

 

Also can I just ask if I am correct in saying that neutrinos are the smallest things in the world?

Edited by oliholbourns
Link to comment
Share on other sites

2 minutes ago, oliholbourns said:

Also can I just ask if I am correct in saying that neutrinos are the smallest things in the world?

!

Moderator Note

You can ask that in the Physics forum. (No, they are the same size as all other fundamental particles)

 
Link to comment
Share on other sites

  • 3 weeks later...
On 11/28/2019 at 11:43 AM, oliholbourns said:

Well, first of all, we need to know is it a straight line? then, as druS mentioned, we may use the equation y = mx + c for a straight line.

 

Also can I just ask if I am correct in saying that neutrinos are the smallest things in the world?

I would take "line" rather than "curve" to mean "straight line".

Also, do not "hijack" someone else's thread to ask an unrelated question.  Start your own thread.  (As Strange said, in the Physics forum, not Math.)

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.