Given:
The slope of the line = m = -2/3
The line passes through the point (3, 10)
We will write the equation of the line with the point-slope form:
[tex]\begin{gathered} y-k=m\cdot(x-h) \\ y-10=-\frac{2}{3}(x-3) \end{gathered}[/tex]Convert the point-slope form into the slope-intercept form
Solve the equation for y
[tex]\begin{gathered} y-10=-\frac{2}{3}x-\frac{2}{3}\cdot(-3) \\ y-10=-\frac{2}{3}x+2 \\ y=-\frac{2}{3}x+2+10 \\ \\ y=-\frac{2}{3}x+12 \end{gathered}[/tex]so, the answer will be:
[tex]y=-\frac{2}{3}x+12[/tex]