ANSWER and EXPLANATION
We want to write the equation of the line that passes through (9, -4) and has a slope of -2/3.
To do that, we will use the point-slope method of writing a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]where (x1, y1) = (9, -4)
m = slope = -2/3
Therefore, we have:
[tex]\begin{gathered} y\text{ - (-4) = }\frac{-2}{3}(x\text{ - 9)} \\ y\text{ + 4 = }\frac{-2}{3}x\text{ + 6} \\ \Rightarrow\text{ y = }\frac{-2}{3}x\text{ + 6 - 4} \\ y\text{ = }\frac{-2}{3}x\text{ + 2} \end{gathered}[/tex]