Question

Write an equation of the line that passes through (-4,-1) and is perpendicular to the line y=4/3x+6

Answer 1

Answer:

$y=-\dfrac{3}{4}x-4.$

Step-by-step explanation:

If needed line is perpendicular to the line $y=\dfrac{4}{3}x+6,$ then its slope satisfies condition

$m\cdot \dfrac{4}{3}=-1\Rightarrow m=-\dfrac{3}{4}.$

Then the equation of needed line will have look

$y=-\dfrac{3}{4}x+b.$

Since this line passes through the point (-4,-1), then

$-1=-\dfrac{3}{4}\cdot (-4)+b,\\ \\-1=3+b,\\ \\b=-1-3=-4.$

Hence, the equation is

$y=-\dfrac{3}{4}x-4.$