Straight Line — Maths STD 11 Science — Question

Equation of the line in two point form is $\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

∴ The equation of the required line is

$\begin{aligned} & \frac{y-1}{2-1}=\frac{x-2}{3-2} \\ & \therefore \frac{y-1}{1}=\frac{x-2}{1} \\ & \therefore y-1=x-2 \\ & \therefore y=x-1\end{aligned}$

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