# Chapter 3 - Determinants - Review Exercises - Page 140: 68

the equation of the line is $$2y+3x-16=0.$$

#### Work Step by Step

The equation of the line is given by $$\left|\begin{array}{rrr}{x} & {y} & {1} \\ {2} & {5} & {1} \\ {6} & {-1} & {1}\end{array}\right|= 0.$$ So, we have $$\left|\begin{array}{rrr}{x} & {y} & {1} \\ {2} & {5} & {1} \\ {6} & {-1} & {1}\end{array}\right|= x(5+1)-y(2-6)+(-2-30)=4y+6x-32=0.$$ Hence, the equation of the line is $$2y+3x-16=0.$$

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