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Georgiy
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  • 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
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  • 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
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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)

 
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  • 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.)

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