Answer:
[tex]y=-\frac{7}{2}x+8[/tex]
Step-by-step explanation:
Given the equation
[tex]y\:=\:\frac{2}{7}x+9[/tex]
comparing the equation with the slope-intercept form
[tex]y =mx+b[/tex]
Here,
so the slope of the line is 2/7
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
the slope of the perpendicular line will be: -7/2
Therefore, the point-slope form of the equation of the perpendicular line that goes through (4,-6) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-6\right)=\frac{-7}{2}\left(x-4\right)[/tex]
[tex]y+6=\frac{-7}{2}\left(x-4\right)[/tex]
[tex]y+6-6=\frac{-7}{2}\left(x-4\right)-6[/tex]
[tex]y=-\frac{7}{2}x+8[/tex]
