Question

Please number 3,4 and 5 Thank you!)

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=48\\--------------------------------\\8x+12y=48\qquad|-8x\\12y=-8x+48\qquad|:12\\y=(-8)/(12)x+(48)/(12)\\----------------------------\\Slope-intercept\ form:\\\\y=(-2)/(3)x+4\\-----------------------------\\Slope:\\\\m=(-2)/(3)\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\----------------------------------\\y-intercept\to b=4\\\\(0,\ 4)`

`Standard\ form:\\\\-5x-3y=-15\\------------------------------------\\-5x-3y=-15\qquad|+5x\\-3y=5x-15\qquad|:(-3)\\y=(5)/(-3)x+(-15)/(-3)\\---------------------------------------\\Slope-intercept\ form:\\\\y=-(5)/(3)x+5\\------------------------------\\Slope:\\\\m=(5)/(-3)\begin{array}{ccc}\uparrow\\\leftarrow\\\end{array}\\--------------------------------\\y-intercept\to b=5\\\\(0,\ 5)`

`Standard\ form:\\\\14x+6y=42\\---------------------------------\\14x+6y=42\qquad|-14x\\6y=-14x+42\qquad|:6\\y=(-14)/(6)x+(42)/(6)\\----------------------------\\Slope-intercept\ form:\\\\y=-(7)/(3)x+7\\----------------------------\\Slope:\\\\m=(-7)/(3)\begin{array}{ccc}\downarrow\\\rightarrow\\\end{array}\\------------------------------\\y-intercept\to b=7\\\\(0,\ 7)`

Answer 2

`y = 4 - (2)/(3) y`
slope: -2/3
y-int: (0,4)

`y = 5 - (5)/(3) x`
slope: -5/3
y-int:(0,5)

`y = 7 - (7)/(3) x`
slope: -7/3
y-int: (0,7)