Question

Equations, Their Slopes And Y-intercepts.

Answer 1

`Standard\ form:\ Ax+By=C\\\\Slope-intercept\ form:\ y=mx+b\\m-slope,\ b-y-intercept`

`Slope:\ m=(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`

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`Standard\ form:\\\\8x-12y=24\\-------------------------------------\\8x-12y=24\qquad|-8x\\-12y=-8x+24\qquad|:(-12)\\y=(-8)/(-12)x+(24)/(-12)\\-------------------------\\Slope-intercept\ form:\\\\y=(2)/(3)x-2\\------------------------------\\Slope:\\\\m=(2)/(3)\begin{array}{ccc}\uparrow\\\rightarrow\\\end{array}\\----------------------------\\y-intercept\to b=-2\\\\(0,\ -2)`

`Standard\ form:\\\\5x+4y=20\\---------------------------------\\5x+4y=20\qquad|-5x\\4y=-5x+20\qquad|:4\\y=(-5)/(4)x+(20)/(4)\\-----------------------\\Slope-intercept\ form:\\\\y=(-5)/(4)x+5\\--------------------------\\Slope:\\\\m=(-5)/(4)\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\---------------------------\\y-intercept\to b=5\\\\(0,\ 5)`

`Standard\ form:\\\\4x+14y=28\\-----------------------------------\\4x+14y=28\qquad|-4x\\14y=-4x+28\qquad|:14\\y=(-4)/(14)x+(28)/(4)\\-------------------------------\\Slope-intercept\ form:\\\\y=-(2)/(7)x+7\\----------------------------\\Slope:\\\\m=(-2)/(7)\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\-------------------------\\y-intexrcept\to b=7\\\\(0,\ 7)`