Question

How do you convert 3x+2y=6 into slope intercept form?​

Answer 1

pretty much by simply solving for "y".

`\bf 3x+2y=6\implies 2y=-3x+6\implies y=\cfrac{-3x+6}{2} \\\\\\ \underset{\textit{distributing the denominator}}{y=\cfrac{-3x}{2}+\cfrac{6}{2}~\hfill }\implies y=-\cfrac{3}{2}x+3\impliedby \begin{array} \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}`

Answer 2

y = -3/2 x +3

Explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

3x+2y = 6

Subtract 3x from each side

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

2y = -3x+6

Divide each side by 2

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

y = -3/2 x +3

This is in slope intercept form where the slope is -3/2 and the y intercept is 3