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:\\\\6x-24y=-48\\--------------------------\\6x-24=-48\qquad|-6x\\-24y=-6x-48\qquad|:(-24)\\y=(-6)/(-24)x+(-48)/(-24)\\--------------------------------\\Slope-intercept\ form:\\\\y=(1)/(4)x+2\\---------------------------\\Slope:\\\\m=(1)/(4)\begin{array}{ccc}\uparrow\\\rightarrow\\\end{array}\\------------------------------\\y-intercept\to b=2\\\\(0,\ 2)`

`Standard\ form:\\\\6y+10x=42\\---------------------------------\\6y+10x=42\qquad|-10x\\6y=-10x+42\qquad|:6\\y=(-10)/(6)x+(42)/(6)\\----------------------------\\Slope-intercept\ form:\\\\y=(-5)/(3)x+7\\----------------------\\Slope:\\\\m=(-5)/(3)\begin{array}{ccc}\downarrow\\\rightarrow\end{array}\\-------------------------------\\y-intercept\to b=7\\\\(0,\ 7)`

`Standard\ form:\\\\-3y+7x=21\\--------------------------\\-3y+7x=21\qquad|-7x\\-3y=-7x+21\qquad|:(-3)\\y=(-7)/(-3)x+(21)/(-3)\\-------------------------------\\Slope-intercept\ form:\\\\y=(7)/(3)x-7\\-------------------------\\Slope:\\\\m=(7)/(3)}\begin{array}{ccc}\uparrow\\\rightarrow\end{array}\\------------------------------------\\y-intercept\to b=-7\\\\(0,\ -7)`