Question

Find the equation of the line perpendicular to y= 3x - 6 that runs through the point (-1, -3).

Answer 1

The equation of the line is;

`y=-(1)/(3)x-(10)/(3)`

Step-by-step explanation:

Given that the line is perpendicular to the equation;

`y=3x-6`

So, the slope of the line will be the negative inverse of the slope of the equation above;

`m=-(1)/(3)`

Also, the line passes through the point;

`(-1,-3)`

Applying the point-slope form of linear equation;

`y-y_1=m(x-x_1)`

Substituting the values of the slope and coordinates;

`\begin{gathered} y-(-3)=-(1)/(3)(x-(-1)) \\ y+3=-(1)/(3)(x+1) \\ y+3=-(1)/(3)x-(1)/(3) \\ y=-(1)/(3)x-(1)/(3)-3 \\ y=-(1)/(3)x-3(1)/(3) \\ y=-(1)/(3)x-(10)/(3) \end{gathered}`

Therefore, the equation of the line is;

`y=-(1)/(3)x-(10)/(3)`