## Algebra and Trigonometry 10th Edition

$2x+6y -13=0$ or, $y=-\dfrac{x}{3}+\dfrac{13}{6}$
The general form of a matrix of order $3 \times 3$ is: $\begin{bmatrix} a & b & c \\ d & e & f \\ g & h& i \end{bmatrix}=a(ei-fh) -b(di-fg)+c(dh-eg)$ Use the formula for a line passing through two points, $(a,b)$ and $(c,d)$. $\begin{vmatrix} x & y & 1 \\ a & c & 1 \\ b & d & 1 \end{vmatrix} =0$ Now, $\begin{bmatrix} x & y & 1 \\ -2.5 & 3 & 1 \\ 3.5 & 1 & 1 \end{bmatrix} =0$ or, $2x+6y -13=0$ or, $y=-\dfrac{x}{3}+\dfrac{13}{6}$