We are given the following equation
[tex]2y=3x+6[/tex]We are asked to find out the slope of this equation.
We know that the slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope of the equation and b is the y-intercept of the equation.
So we need to convert the given equation into the slope-intercept form.
[tex]\begin{gathered} 2y=3x+6 \\ \frac{2y}{2}=\frac{3x}{2}+\frac{6}{2} \\ y=\frac{3x}{2}+3 \end{gathered}[/tex]As you can see now the equation is converted into slope-intercept form.
The slope of the equation is m = 3/2
[tex]m=\frac{3}{2}[/tex]