# Chapter 10 - Review Exercises - Page 763: 115

$x-2y+4=0$

#### Work Step by Step

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 going through two points, $(a,b)$ and $(c,d)$ $\begin{vmatrix} x & y & 1 \\ a & c & 1 \\ b & d & 1 \end{vmatrix} =0$ Now, $D=det \begin{bmatrix} x & y & 1 \\ -4 & 0 & 1 \\ 4 & 4 & 1 \end{bmatrix}$ or, $-4x+8y-16=0$ So, we have: $x-2y+4=0$

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