Question

Please number 3,4 and 5 Thank you!)

Answer 1

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

$Slope:\ m=\dfrac{b}{a}\\\\\uparrow b\ units\ if\ b > 0\\\downarrow b\ units\ if\ b < 0\\\leftarrow a\ units\ if\ a < 0\\\rightarrow a\ units\ if\ a > 0$

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

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

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

Answer 2

$y = 4 - \frac{2}{3} y$
slope: -2/3
y-int: (0,4)
$y = 5 - \frac{5}{3} x$
slope: -5/3
y-int:(0,5)
$y = 7 - \frac{7}{3} x$
slope: -7/3
y-int: (0,7)