Answer:
[tex]y=\frac{3}{2}x-11[/tex]
Step-by-step explanation:
We have been given an equation [tex]y=-\frac{2}{3}x+5[/tex]. We are asked to find the equation of line perpendicular to our given equation and passes through point (8,1).
We know that the slope of a perpendicular line to a given line is negative reciprocal of the slope of given line. So the slope of perpendicular line to the line [tex]y=-\frac{2}{3}x+5[/tex] will be negative reciprocal of [tex]-\frac{2}{3}[/tex].
[tex]\text{negative reciprocal of }-\frac{2}{3}=-(-\frac{3}{2})[/tex]
[tex]\text{negative reciprocal of }-\frac{2}{3}=\frac{3}{2}[/tex]
Upon substituting [tex]m=\frac{3}{2}[/tex] and coordinates of point (8,1) in slope intercept form of equation we will get,
[tex]1=\frac{3}{2}*8+b[/tex]
[tex]1=3*4+b[/tex]
[tex]1=12+b[/tex]
[tex]1-12=12-12+b[/tex]
[tex]-11=b[/tex]
Therefore, the equation [tex]y=\frac{3}{2}x-11[/tex] represents the equation of line perpendicular to our given line.
