Question

Find the equation of a straight line passingthrough the points (1, 1) and (2, -1).

Answer 1

Using two-points form equation of a line formula as shown below

$\frac{y-y_1}{x-x_1}=\frac{y_2-y__1}{x_2-x_1}$

From the question, we have that:

$\begin{gathered} (1,1)\rightarrow x_1=1,y_1=1 \\ (2,-1)\rightarrow x_2=2,y_2=-1 \end{gathered}$

Substitute the coordinates values above in the two-points form equation

$\frac{y-1}{x-1}=\frac{-1-1}{2-1}$$\frac{y-1}{x-1}=\frac{-2}{1}$

Cross multiply and simplify the equation

$\begin{gathered} 1(y-1)=-2(x-1) \\ y-1=-2x+2 \\ y=-2x+2+1 \\ y=-2x+3 \end{gathered}$

Hence, the equation of the straight line is y = -2x + 3