[tex]Standard\ form:\ Ax+By=C\\\\Slope-intercept\ form:\ y=mx+b\\m-slope,\ b-y-intercept[/tex]
[tex]Slope:\ m=\dfrac{b}{a}\\\\\uparrow b\ units\ if\ b > 0\\\downarrow b\ units\ if\ b < 0\\\leftarrow a\ units\ if\ a < 0\\\rightarrow a\ units\ if\ a > 0[/tex]
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[tex]Standard\ form:\\\\8x-12y=24\\-------------------------------------\\8x-12y=24\qquad|-8x\\-12y=-8x+24\qquad|:(-12)\\y=\dfrac{-8}{-12}x+\dfrac{24}{-12}\\-------------------------\\Slope-intercept\ form:\\\\y=\dfrac{2}{3}x-2\\------------------------------\\Slope:\\\\m=\dfrac{2}{3}\begin{array}{ccc}\uparrow\\\rightarrow\\\end{array}\\----------------------------\\y-intercept\to b=-2\\\\(0,\ -2)[/tex]
[tex]Standard\ form:\\\\5x+4y=20\\---------------------------------\\5x+4y=20\qquad|-5x\\4y=-5x+20\qquad|:4\\y=\dfrac{-5}{4}x+\dfrac{20}{4}\\-----------------------\\Slope-intercept\ form:\\\\y=\dfrac{-5}{4}x+5\\--------------------------\\Slope:\\\\m=\dfrac{-5}{4}\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\---------------------------\\y-intercept\to b=5\\\\(0,\ 5)[/tex]
[tex]Standard\ form:\\\\4x+14y=28\\-----------------------------------\\4x+14y=28\qquad|-4x\\14y=-4x+28\qquad|:14\\y=\dfrac{-4}{14}x+\dfrac{28}{4}\\-------------------------------\\Slope-intercept\ form:\\\\y=-\dfrac{2}{7}x+7\\----------------------------\\Slope:\\\\m=\dfrac{-2}{7}\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\-------------------------\\y-intexrcept\to b=7\\\\(0,\ 7)[/tex]
