Choose the correct graph to fit the equation 3y=2x+3

y = 2/3x + 1    

Step-by-step explanation:

3y = 2x + 3           Divide all by 3

3       3      3

y = 2/3x + 1           Slope is 2/3

Step-by-step explanation:

The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. In this expression m is called the slope of the line and is related to the inclination of the line. B is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.

So to get to the model y=m*x+b you must isolate the value of y. For that, each term is divided by 3 to get:

Then, compared to the model previously proposed, 2/3 is the value of the slope and 1 is the value of b, which is the independent term. This last value, as mentioned, indicates the point of intersection between the line and the "y" axis.  The graph of the line with these values is attached.