Answer:
a) standard form of [tex]y=\frac{2}{3}x+3[/tex] is 2x-3y=-9 Hence Option 3 is correct option.
b) standard form of [tex]6-y=-5x+8\\[/tex] is 5x-y=2 Hence Option 2 is correct option.
c) standard form of [tex]y-3=4(x-3)\\[/tex] is 4x-y=9 Hence Option 4 is correct option.
d) standard form of [tex]-\frac{7}{6}x+1=y[/tex] is 7x+6y=6 Hence Option 1 is correct option.
Step-by-step explanation:
The standard form of equation is Ax+By=C
So, we will convert each given question to Ax+By=C and then match the results.
a) [tex]y=\frac{2}{3}x+3[/tex]
Solving:
[tex]y=\frac{2}{3}x+3\\y=\frac{2x+9}{3}\\3y=2x+9\\2x-3y=-9[/tex]
So, standard form is 2x-3y=-9 Hence Option 3 is correct option for this question.
b) [tex]6-y=-5x+8\\[/tex]
Solving:
[tex]6-y=5x+8\\5x-y=8-6\\5x-y=2[/tex]
So, standard form is 5x-y=2 Hence Option 2 is correct option for this question.
c) [tex]y-3=4(x-3)\\[/tex]
Solving:
[tex]y-3=4(x-3)\\y-3=4x-12\\4x-y=12-3\\4x-y=9[/tex]
So, standard form is 4x-y=9 Hence Option 4 is correct option for this question.
d) [tex]-\frac{7}{6}x+1=y[/tex]
solving
[tex]-\frac{7}{6}x+1=y \\\frac{-7x+1*6}{6}=y\\ \frac{-7x+6}{6}=y\\-7x+6=6y\\Multiplying \ by \ (-1) \ on \ both \ sides:\\7x-6=-6y\\7x+6y=6[/tex]
So, standard form is 7x+6y=6 Hence Option 1 is correct option for this question.
