Find the equation of the line that passes through (2,3) and (-3,3).

Let us suppose that  a line y = mx +c passes through the points (2,3) and (-3,3). Now our work is to find m and c  by the conditions that the points (2,3) and (3, -3) satisfy the equation y = mx+c, or mx+c = y.

Since (2,3) satisfy mx+c = y, put x=2 and y = 3.

m(2)+c = 3.

2m+c = 3..................(1)

Similarly, the other point (3,3) also should satisfy mx+c = y. So,

3m+c = 3..................(2)

Now we solve for m and n from equations (1) and (2):

Eq(3)- Eq(1) eliminates c.

(3m+c)-(2m+c) = 3-3

m = 0.

Substituting m =0 in (1), c = 3.

So y= mx+c now becomes, y = 0x+3 . Or y =3 is the equation that passes through (2,3) and (3,3)..