Question

Which function has the same y intercept as the function y = 2/3x - 3 ?

Answer 1

$\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf 6x-7y=21\implies -7y=-6x+21\implies y=\cfrac{-6x+21}{-7}\implies y=\cfrac{6x-21}{7} \\\\\\ \stackrel{\textit{distributing the denominator}}{y=\cfrac{6x}{7}-\cfrac{21}{7}}\implies y=\cfrac{6}{7}x\stackrel{\stackrel{b}{\downarrow }}{-3}$

Answer 2

y=mx+b

b=y intercept

get into this form with no coefficient to y

Original: yint: -3

1)x+4y=12

4y=-x+12

y=-.25+3

b=3

2)2/3x+3y=-3

3y=2/3x-3

y={doesn't matter}x-1

b=-1

3)-2/3x+3y=6

3y=-2/3x+6

y={doesn't matter} +2

b=2

4) 6x-7y=21

-7y=-6x+21

y=6/7-3

b=-3

4 is the answer