Answer:
[tex]y=-\dfrac{3}{4}x-4.[/tex]
Step-by-step explanation:
If needed line is perpendicular to the line [tex]y=\dfrac{4}{3}x+6,[/tex] then its slope satisfies condition
[tex]m\cdot \dfrac{4}{3}=-1\Rightarrow m=-\dfrac{3}{4}.[/tex]
Then the equation of needed line will have look
[tex]y=-\dfrac{3}{4}x+b.[/tex]
Since this line passes through the point (-4,-1), then
[tex]-1=-\dfrac{3}{4}\cdot (-4)+b,\\ \\-1=3+b,\\ \\b=-1-3=-4.[/tex]
Hence, the equation is
[tex]y=-\dfrac{3}{4}x-4.[/tex]
