Question

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

Answer 1

Given, A(2, 1) and B(3, 2)

Equation of the line in two point form is

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

∴ The equation of the required 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

Alternate Method:

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