Question

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

(1) x + 4y = 12
(2) 2/3x + 3y = -3
(3) -2/3x + 3y = 6
(4) 6x - 7y = 21

Answer 1

`\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}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