Find the equations of line joining points #(-2,3)# and #(1,4)#?
The equation for line joining two points
Let the slope intercept form of equation be
here we do not know the slope
What we know is that this passes through the two coordinate pairs, say
As such we have three equations
Now using these let us eliminate
subtracting (2) from (1), we get
and subtracting (2) from (3), we get
Dividing (4) by (5)
As the two points are
For slope m and intercept c, the equation is y = m x +c.
The slope intercept form for coordinates is (x, m x +c ).
The slope of the line through the given points is
Also, from (1, 4). 4 = i/3(1) + c. So, c = 11/3.
So, the answer is
The equation of the line is:
If you are given the coordinates of 2 points on a line, substituting them into the formula below allows you to find the equation immediately. In the process you also calculate the slope.