Question

What is the slope and the y-intercept of each equation

(1) 12x + 3y = 9
(2) 6x - 2y =2
(3) 2x + 5y = 10
(4) 9x - 3y = -1
(5) 4y + 6x =2
(6) 8y -2x = 5
(7) 5x + 5y = 3
(8) -4y = 16
(9) 6x = 12

Answer 1

`y=mx+b\\m\ \ \rightarrow\ \ the\ slope\\b\ \ \rightarrow\ \ y-intercept\\---------------------------\\1)\ \ 12x+3y=9\ \ \ \Rightarrow\ \ \ 3y=-12x+9\ /:3\\.\ \ \ \ y=-4x+3\ \ \ \Rightarrow\ \ \ m=-4\ \ \ \ \ and\ \ \ \ \ b=3\\\\2)\ \ 6x-2y=2\ \ \ \Rightarrow\ \ \ -2y=-6x+2\ /:(-2)\\.\ \ \ \ y=3x-1\ \ \ \Rightarrow\ \ \ m=3\ \ \ \ \ and\ \ \ \ \ b=-1\\\\3)\ \ 2x+5y=10\ \ \ \Rightarrow\ \ \ 5y=-2x+10\ /:5\\.\ \ \ \ y=- (2)/(5) x+2\ \ \ \Rightarrow\ \ \ m=- (2)/(5)\ \ \ \ \ and\ \ \ \ \ b=2\\\\`


`4)\ \ 9x-3y=-1\ \ \ \Rightarrow\ \ \ -3y=-9x-1\ /:(-3)\\.\ \ \ \ y=3 x+ (1)/(3)\ \ \ \Rightarrow\ \ \ m= 3\ \ \ \ \ and\ \ \ \ \ b=(1)/(3)\\\\5)\ \ 4y+6x=2\ \ \ \Rightarrow\ \ \ 4y=-6x+2\ /:4\\.\ \ \ \ y=-(3)/(2) x+ (1)/(2)\ \ \ \Rightarrow\ \ \ m= -(3)/(2)\ \ \ \ \ and\ \ \ \ \ b=(1)/(2)\\\\6)\ \ 8y-2x=5\ \ \ \Rightarrow\ \ \ 8y=2x+5\ /:8\\.\ \ \ \ y=(1)/(4) x+ (5)/(8)\ \ \ \Rightarrow\ \ \ m=(1)/(4)\ \ \ \ \ and\ \ \ \ \ b=(5)/(8)\\\\`


`7)\ \ 5x+5y=3\ \ \ \Rightarrow\ \ \ 5y=-5x+3\ /:5\\.\ \ \ \ y= -x+ (3)/(5)\ \ \ \Rightarrow\ \ \ m=-1\ \ \ \ \ and\ \ \ \ \ b=(3)/(5)\\\\8)\ \ -4y=16\ /:(-4)\\.\ \ \ \ y= -4\ \ \ \Rightarrow\ \ \ m=0\ \ \ \ \ and\ \ \ \ \ b=-4\\\\8)\ \ 6x=12\ /:6\\.\ \ \ \ x=2\ \ \ \Rightarrow\ \ \ not\ exist:\ \ \ the\ slope\ \ \ and\ \ \ the\ y-intercept`

Answer 2

`The\ slope-intercept\ form:y=mx+b\\\\m-the\ slope;\ b-y-intercept`



`(1)\\12x+3y=9\\3y=-12x+9\ \ \ \ |divide\ both\ sides\ by\ 3\\y=-4x+3\\\boxed{m=-4;\ b=3}\\\\(2)\\6x-2y=2\\-2y=-6x+2\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\\y=3x-1\\\boxed{m=3;\ b=-1}`


`(3)\\2x+5y=10\\5y=-2x+10\ \ \ \ |divide\ both\ sides\ by\ 5\\y=-(2)/(5)x+2\\\boxed{m=-(2)/(5);\ b=2}\\\\(4)\\9x-3y=-1\\-3y=-9x-1\ \ \ \ |divide\ both\ sides\ by\ (-3)\\y=3x+(1)/(3)\\\boxed{m=3;\ b=(1)/(3)}`


`(5)\\4y+6x=2\\4y=-6x+2\ \ \ \ |divide\ both\ sides\ by\ 4\\y=-(6)/(4)x+(2)/(4)\\y=-(3)/(2)x+(1)/(2)\\\boxed{m=-(3)/(2);\ b=(1)/(2)}\\\\(6)\\8y-2x=5\\8y=2x+5\ \ \ \ |divide\ both\ sides\ by\ 8\\y=(2)/(8)x+(5)/(8)\\y=(1)/(4)x+(5)/(8)\\\boxed{m=(1)/(4);\ b=(5)/(8)}`


`(7)\\5x+5y=3\\5y=-5x+3\ \ \ \ |divide\ both\ sides\ by\ 5\\y=-x+(3)/(5)\\\boxed{m=-1;\ b=(3)/(5)}\\\\(8)\\-4y=16\ \ \ \ |divide\ both\ sides\ by\ (-4)\\y=-4\\\boxed{m=0;\ b=-4}\\\\(9)\\6x=12\ \ \ \ |divide\ both\ sides\ by\ 6\\x=2\\\boxed{m\ and\ b\ not\ exist}`