Question

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

Answer 1

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

answer
 y = -2/3x + 2

Answer 2

we know that

The equation of the line into slope-intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$2x+3y=6$

Isolate the variable y

$3y=-2x+6$

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

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

the slope is $m=-\frac{2}{3}$

the y-intercept is $b=2$

the answer in the attached figure