Question

Line y = mx + c passes through the points A(2, 1) and B(3, 2). Determine m and c.

Answer 1

Given, A(2, 1) and B(3, 2).
Equation of a line in two point form is

`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`

∴ the equation of the passing through A and B line is

`(y - 1)/(2 - 1) = (x - 2)/(3 - 2)`

∴ `(y - 1)/1 = (x - 2)/1`

∴ y – 1 = x – 2
∴ y = x – 1
Comparing this equation with y = mx + c, we get
m = 1 and c = – 1

Answer 2

Points A(2, 1) and B(3, 2) lie on the line y = mx + c.
∴ They must satisfy the equation.
∴ 2m + c = 1          ...(i)
and 3m + c = 2     ...(ii)
equation (ii) equation (i) gives m = 1
Substituting m = 1 in (i), we get
2(1) + c = 1
∴ c = 1 – 2 = – 1