Question

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1).

Answer 1

solve for y first :)

Answer 2

The equation of the line is :
\[\Large y=-3x+7\]
So the slope is -3
The slope m of a perpendicular line to this line verify :
\[\Large m\times(-3)=-1\]
So :
\[\Large m=\frac13\]
So the equation is :
\[\Large y=mx+b=-\frac13x+b\]
For finding b, we have the point (6.-1) is from the line so :
\[\Large -1=\frac13\times 6+b\]
So :
\[\Large b=-1-2=-3\]
So the equation of line :
\[\Large y=-\frac13x-3\]
Or :
\[\Large 3y+x+9=0\]