Question

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

Answer 1

`y=-(3)/(4)x-4.`

Explanation:

If needed line is perpendicular to the line
`y=(4)/(3)x+6,` then its slope satisfies condition

`m\cdot (4)/(3)=-1\Rightarrow m=-(3)/(4).`

Then the equation of needed line will have look

`y=-(3)/(4)x+b.`

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

`-1=-(3)/(4)\cdot (-4)+b,\\ \\-1=3+b,\\ \\b=-1-3=-4.`

Hence, the equation is

`y=-(3)/(4)x-4.`