Question

Which of the following points are solutions to the equation y= -2/3x+2

Answers are either

(-2/5,34/15)

(7/2,13/3)

(1/8,23/12)

(8/3,2/3)

Answer 1

`y=-(2)/(3)x+2\\\\\left(-(2)/(5);\ (34)/(15)\right)\to x=-(2)/(5);\ y=(34)/(15)\\\\for\ x=-(2)/(5)\to y=-(2)/(3)\cdot\left(-(2)/(5)\right)+2=(4)/(15)+2=(4)/(15)+(30)/(15)=(34)/(15)\\CORRECT\\\\\left((7)/(2);\ (13)/(3)\right)\to x=(7)/(2);\ y=(13)/(3)\\\\for\ x=(7)/(2)\to y=-(2)/(3)\cdot(7)/(2)+2=-(7)/(3)+2=-(7)/(3)+(6)/(3)=-(1)/(3)\\eq(13)/(3)\\INCORRECT`

`\left((1)/(8);\ (23)/(12)\right)\to x=(1)/(8);\ y=(23)/(12)\\\\for\ x=(1)/(8)\to y=-(2)/(3)\cdot(1)/(8)+2=-(1)/(12)+2=-(1)/(12)+(24)/(12)=(23)/(12)\\CORRECT\\\\\left((8)/(3);\ (2)/(3)\right)\to x=(8)/(3);\ y=(2)/(3)\\\\for\ x=(8)/(3)\to y=-(2)/(3)\cdot(8)/(3)+2=-(16)/(9)+2=-(16)/(9)+(18)/(9)=(2)/(9)\\eq(2)/(3)\\INCORRECT`

Answer: (-2/5,34/15) and (1/8,23/12).