The given equation is
[tex]y=\frac{5}{9}x+9[/tex]The slope of the given equation is 5/9. Remember that the slope is the coefficient of x.
Given that the new line must be parallel to the given equation, then the new line has a slope of 5/9 too.
Then, we use the point (18,-2), the slope, and the point-slope formula.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{5}{9}(x-18) \\ y+2=\frac{5}{9}x-10 \\ y=\frac{5}{9}x-10-2 \\ y=\frac{5}{9}x-12 \end{gathered}[/tex]
