The equation of the line in Slope-Intercept form is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case, you have the following equation of a line:
[tex]2x+3y=10[/tex]
To write it in Slope-Intercept form, you must solve for "y":
[tex]\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-\frac{2}{3}x+\frac{10}{3} \end{gathered}[/tex]
So you can see that its slope is:
[tex]m_1=-\frac{2}{3}[/tex]
The slopes of perpendicular lines are opposite reciprocals, then you can determine that the slope of the other line is:
[tex]m_2=\frac{3}{2}[/tex]
You can see in the picture that the only equation that has this slope is the one shown
