What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6

Solution:

This standard form of a line is Ax + By + C = 0

The standard slope-intercept form is y = mx+b

where m is the slope and b is the y-intercept of the line.

a) 2x + 3y = -6

We rewrite to get the slope standard form.

3y= -6-2x

y= (-6-2x)/3

y= -2/3 x -2

This is in standard equation form y = mx+b

b) 2x + 3y = 6

This is of the form Ax + By + C = 0

3y= 6-2x

y= (6-2x)/3

y= -2/3 x +2

What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6

Summary:

a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.

b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.