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where would you graph this equation; 2x +3y + 6 = 0

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2 Answers

Hi again Sister Serena;
2x +3y + 6 = 0
I would prefer this equation to be in the format of...
y=mx+b
m=slope, the change in y, also known as rise, divided by the change in x, also known as run.
b=y-intercept, the value of y when x=0.
2x +3y + 6 = 0
Let's subtract (2x+6) from both sides...
-(2x+6)+2x+3y+6=0-(2x+6)
3y=-2x-6
Let's divide both sides by 3...
(3y)/3=(-2x-6)/3
y=(-2/3)x-2
The slope is -2/3 and the y-intercept is -2.
According to protocol, the slope is represented as -2/3 in that the negative sign is before the numerator.  However, the field of mathematics has a problem.  The negative sign should be before the 3, 2/-3,  This is because as the line rises positively 2 units, it runs negatively to the left 3 units.
 
Draw your line beginning with (0,-2), then rise 2 and move to the left 3 to find the next point.
If you find the coordinate of 2 points on a line and connect then extend, you will have the graph of the line.
 
   The easiest of 2 points are intercepts.
 
       2X + 3 y + 6 = 0
 
        X intercept :
 
         2X +3(0) = -6
 
         ( -3, 0)
 
          Y intercept:
         
        2(0) + 3Y = -6
 
            Y = -2
 
           (0, -2)
 
       Locate the intercepts and graph your line.