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

Answers

Answer 1

Answer: $The\ slope-intercept\ form:y=mx+b\n\nm-the\ slope;\ b-y-intercept$

$(1)\n12x+3y=9\n3y=-12x+9\ \ \ \ |divide\ both\ sides\ by\ 3\ny=-4x+3\n\boxed{m=-4;\ b=3}\n\n(2)\n6x-2y=2\n-2y=-6x+2\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\ny=3x-1\n\boxed{m=3;\ b=-1}$

$(3)\n2x+5y=10\n5y=-2x+10\ \ \ \ |divide\ both\ sides\ by\ 5\ny=-(2)/(5)x+2\n\boxed{m=-(2)/(5);\ b=2}\n\n(4)\n9x-3y=-1\n-3y=-9x-1\ \ \ \ |divide\ both\ sides\ by\ (-3)\ny=3x+(1)/(3)\n\boxed{m=3;\ b=(1)/(3)}$

$(5)\n4y+6x=2\n4y=-6x+2\ \ \ \ |divide\ both\ sides\ by\ 4\ny=-(6)/(4)x+(2)/(4)\ny=-(3)/(2)x+(1)/(2)\n\boxed{m=-(3)/(2);\ b=(1)/(2)}\n\n(6)\n8y-2x=5\n8y=2x+5\ \ \ \ |divide\ both\ sides\ by\ 8\ny=(2)/(8)x+(5)/(8)\ny=(1)/(4)x+(5)/(8)\n\boxed{m=(1)/(4);\ b=(5)/(8)}$

$(7)\n5x+5y=3\n5y=-5x+3\ \ \ \ |divide\ both\ sides\ by\ 5\ny=-x+(3)/(5)\n\boxed{m=-1;\ b=(3)/(5)}\n\n(8)\n-4y=16\ \ \ \ |divide\ both\ sides\ by\ (-4)\ny=-4\n\boxed{m=0;\ b=-4}\n\n(9)\n6x=12\ \ \ \ |divide\ both\ sides\ by\ 6\nx=2\n\boxed{m\ and\ b\ not\ exist}$

Answer 2

Answer: $y=mx+b\nm\ \ \rightarrow\ \ the\ slope\nb\ \ \rightarrow\ \ y-intercept\n---------------------------\n1)\ \ 12x+3y=9\ \ \ \Rightarrow\ \ \ 3y=-12x+9\ /:3\n.\ \ \ \ y=-4x+3\ \ \ \Rightarrow\ \ \ m=-4\ \ \ \ \ and\ \ \ \ \ b=3\n\n2)\ \ 6x-2y=2\ \ \ \Rightarrow\ \ \ -2y=-6x+2\ /:(-2)\n.\ \ \ \ y=3x-1\ \ \ \Rightarrow\ \ \ m=3\ \ \ \ \ and\ \ \ \ \ b=-1\n\n3)\ \ 2x+5y=10\ \ \ \Rightarrow\ \ \ 5y=-2x+10\ /:5\n.\ \ \ \ y=- (2)/(5) x+2\ \ \ \Rightarrow\ \ \ m=- (2)/(5)\ \ \ \ \ and\ \ \ \ \ b=2\n\n$

$4)\ \ 9x-3y=-1\ \ \ \Rightarrow\ \ \ -3y=-9x-1\ /:(-3)\n.\ \ \ \ y=3 x+ (1)/(3)\ \ \ \Rightarrow\ \ \ m= 3\ \ \ \ \ and\ \ \ \ \ b=(1)/(3)\n\n5)\ \ 4y+6x=2\ \ \ \Rightarrow\ \ \ 4y=-6x+2\ /:4\n.\ \ \ \ y=-(3)/(2) x+ (1)/(2)\ \ \ \Rightarrow\ \ \ m= -(3)/(2)\ \ \ \ \ and\ \ \ \ \ b=(1)/(2)\n\n6)\ \ 8y-2x=5\ \ \ \Rightarrow\ \ \ 8y=2x+5\ /:8\n.\ \ \ \ y=(1)/(4) x+ (5)/(8)\ \ \ \Rightarrow\ \ \ m=(1)/(4)\ \ \ \ \ and\ \ \ \ \ b=(5)/(8)\n\n$

$7)\ \ 5x+5y=3\ \ \ \Rightarrow\ \ \ 5y=-5x+3\ /:5\n.\ \ \ \ y= -x+ (3)/(5)\ \ \ \Rightarrow\ \ \ m=-1\ \ \ \ \ and\ \ \ \ \ b=(3)/(5)\n\n8)\ \ -4y=16\ /:(-4)\n.\ \ \ \ y= -4\ \ \ \Rightarrow\ \ \ m=0\ \ \ \ \ and\ \ \ \ \ b=-4\n\n8)\ \ 6x=12\ /:6\n.\ \ \ \ x=2\ \ \ \Rightarrow\ \ \ not\ exist:\ \ \ the\ slope\ \ \ and\ \ \ the\ y-intercept$

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

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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