Question

What is the slope-intercept form of the liner equation 2x + 3y = 6?

Answer 1

Answer:  $y = -\frac{2}{3}x+2$

Check out the diagram below.

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Work Shown:

$2x + 3y = 6\\\\3y = 6-2x\\\\3y = -2x+6\\\\y = \frac{-2x+6}{3}\\\\y = \frac{-2x}{3}+\frac{6}{3}\\\\y = -\frac{2}{3}x+2$

The steps above show us subtracting 2x from both sides, then we divide both sides by 3 to fully isolate y.

The last equation is in $y = mx+b$ form with $m = -\frac{2}{3}$ as the slope and $b = 2$ as the y intercept.