Question

Equations, Their Slopes And Y-intercepts.

Answer 1

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

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

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

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

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