Question

Equations, Their Slopes And Y-intercepts. Please 9,11 and 12 question! 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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$Standard\ form:\\\\12x-9y=45\\-------------------------------\\12x-9y=45\qquad|-12x\\-9y=-12x+45\qquad|:9\\y=\dfrac{-12}{9}x+\dfrac{45}{9}\\------------------------------\\Slope-intercept\ form:\\\\y=\dfrac{-4}{3}x+5\\--------------------------------\\Slope:\\\\m=\dfrac{-4}{3}\begin{array}{ccc}\downarrow\\\rightarrow\end{array}\\-------------------------\\y-intercept\to b=5\\\\(0,\ 5)$

$Standard\ form:\\\\3y+2x=-15\\-----------------------------------\\3y+2x=-15\qquad|-2x\\3y=-2x-15\qquad|:3\\y=\dfrac{-2}{3}x+\dfrac{-15}{3}\\------------------------------\\Slope-intercept\ form:\\\\y=\dfrac{-2}{3}x-5\\----------------------------------\\Slope:\\\\m=\dfrac{-2}{3}\begin{array}{ccc}\downarrow\\\rightarrow\end{array}\\--------------------------------\\y-intercept\to b=-5\\\\(0,\ -5)$

$Standard\ form:\\\\10x+8y=40\\------------------------------------\\10x+8y=40\qquad|-10x\\8y=-10x+40\qquad|:8\\y=\dfrac{-10}{8}x+\dfrac{40}{8}\\------------------------------\\Slope-intercept\ form:\\\\y=\dfrac{-5}{4}x+5\\---------------------------\\Slope:\\\\m=\dfrac{-5}{4}\begin{array}{ccc}\downarrow\\\rightarrow\end{array}\\------------------------\\y-intercept\to b=5\\\\(0,\ 5)$

Answer 2

Hey there!

(9) 2x-9y=45

... -9y=-2x+45

... y = (2/9)x - 5

Slope = 2/9

y-intercept = (0,-5)

(11) 3y+2x=-15

... 3y=-2x-15

... y = (-2/3)x - 5

Slope = -2/3

y-intercept = (0,-5)

(12) 10x+8y=40

... 8y=-10x+40

... y=(-10/8)x+5

Slope = -5/4 (after simplifying )

y-intercept = (0,5)

Hope my answer helps!