Step-by-step explanation:
consider that (x,y) is a general point on the line (variable), and (x1, y1) is a given fixed point on the line Â
M, the slope of the line may be given as: Â
M = (y - y1) / (x - x1) Â
if you know the value of M, and the values x1 and y1, (which you do, since point (x1, y1) is given to you as a fixed point), Â
you can rearrange the above equation to get the equation of the line Â
the reason for this is that every point (x,y) on the required line will satisfy the above equation ( (x,y) is a general point ) Â
which means this equation is a relation between x and y which gives us the values of x and y which make (x,y) fall on the line Â
this means that the obtained relation is nothing but a representation of the required line, ie equation of the line Â
in the second example, fixed point is (x1, y1) =(1, 0) Â
M = (-4) Â
x1 = 1 Â
y1 = 0 Â
we have, Â
M = (y - y1) / (x - x1) Â
ie (-4) = (y - 0) / (x - 1) Â
ie (-4) = y / (x-1) Â
ie y = -4x + 4 Â
ie [ 4x + y = 4 ] Â
which is the equation of the line Â
the first example is almost the same thing Â
onlhy in this case you have to find the slope M manually Â
M = (y2 - y1) / (x2 - x1) Â
where (x1, y1) and (x2, y2) are given fixed points on the line Â
in the example, Â
M = [ 5 - (-3) ] / [ 3 - 2 ] Â
M = 8 / 1 Â
M = 8 Â
and proceed in a manner similar to the other example