Answer:
[tex]\large\boxed{y=\dfrac{3}{2}x+8}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form:}[/tex]
[tex]y=mx+b\\\\m - slope\\b - y-intercept[/tex]
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
[tex]\text{We have}\ y=-\dfrac{2}{3}x+5\to m_1=-\dfrac{2}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-\frac{2}{3}}=-\left(-\dfrac{3}{2}\right)=\dfrac{3}{2}\\\\\text{We have the equation}\ y=\dfrac{3}{2}x+b.\\\\\text{Put the coordinates of the point (2, 11) to the equation and calculate b}:\\\\11=\dfrac{3}{2}(2)+b\\\\11=3+b\qquad\text{subtract 3 from both sides}\\\\8=b\to b=8\\\\\text{Finally we have}\ y=\dfrac{3}{2}x+8.[/tex]
