Equation Of The Line
Equation Of The Line
In mathematics we have so many fields like geometry, algebra, calculus,
trigonometry etc but in geometry the meaning of line is a straight line which
consists of at least two points and can be extend in both the directions up to
infinity but the condition is we have to extend this in straight manner and no curve
should be present otherwise it is not a line.
Now we are going to learn the meaning of Equation of a Line, so there are various
forms of a straight line like slope intercept form, point slope form etc but we are
going to see standard form of straight line.
Equation of line is Ax + By = C
Where A and B are not equal to 0
In the above equation x and y are coordinates and A, B and C are constants and
also constants A and B are not equal to 0 and also there is no thickness in line
which is property of line.
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Now we are taking an equation and the find out the coordinates after that we plot
these coordinates on graph and we get straight line so the equation of line is 3x +
4y = 2
Now putting x = 0 then we have y = (1/2)
Now putting x = 1 then we have y = (-1/4)
Now putting x = 2 then we have y = (-1)
So now we have three coordinates and that is (x1, y1), (x2, y2) and (x3, y3) ant
their values are (0, 1/2), (1, -1/4) and (2, -1) respectively and now if we plotted
these coordinates on graph then we get straight line so the standard form of line
is Ax + By = C and A and B are not equal to 0.
This standard form is useful when we want to graph any line or it is also used
when we know the y intercept of line or x intercept of line so that we can find the
intercept of other coordinate and get the straight line.
There are also other forms like slope intercept form or point slope form and these
forms are use full when we have to find the slope of line.
Now if the slope of any two lines is same then they are parallel to each other and
if the slope of one line is equal to the negative reciprocal of other line then these
two lines are perpendicular to each other.
So if m1 = m2 then lines are parallel and
If m1 = -1/m2 then line are perpendicular.
Where m = slope of line.
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Now if we want to find the slope of line then we have to know this formula
m = (y1 – y2) / (x1 – x2)
Suppose that we have two coordinates of line, first coordinate is (6, 8) and second
coordinate is (2, 2) now find out the slope of line then putting the values in above
m = (8 - 6) / (6 - 2)
m = 2/4
So by this way we find the slope of any line and also the intercepts of x and y and
when we know the intercepts then we plot this on graph and get line.
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