Question

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

Answer 1

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


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

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

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

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

Answer 2

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

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

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