ANSWER
Equation:
[tex]y=\frac{5}{4}x-1[/tex]Graph:
The red line is the graph of the given line and the green line is the graph of the perpendicular line passing through (8, 9).
EXPLANATION
The equation of the line is given in the slope-intercept form,
[tex]y=-\frac{4}{5}x+2[/tex]The slope is -4/5 and the y-intercept is 2.
Two lines are perpendicular if their slopes are opposite reciprocals of each other. Therefore, a perpendicular line to the given line has a slope of 5/4,
[tex]y=\frac{5}{4}x+b[/tex]There is an infinite number of perpendicular lines, but there is only one that passes through the point (8, 9). Replace x and y with the coordinates of this point in the equation above,
[tex]9=\frac{5}{4}\cdot8+b[/tex]And solve for b,
[tex]\begin{gathered} 9=5\cdot2+b \\ 9=10+b \\ 9-10=b \\ -1=b \end{gathered}[/tex]Hence, the equation of the perpendicular line is,
[tex]y=\frac{5}{4}x-1[/tex]
