Respuesta :

frika

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]

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