The given equation of the line is `y-3=3(x + 1)` .
Rearranging it in the slope-intercept form i.e. `y=mx+b` where `m` is the slope of the line we get:
Thus, slope of the line, `m=3` .
Again, the slope of the perpendicular line is the negative reciprocal of the slope of the original line.
So, slope of the perpendicular line=`-1/3`
Now, use the point-slope form of the equation of the straight line to find the equation of the perpendicular line.
Here, `(x_1,y_1)=(5,1)` and `m=-1/3` . Plug in these values in the above equation to get:
Multiply both sides by `3` :
Therefore, the equation in standard form of a perpendicular line that passes through (5,1) is x+3y=8.
To find the x intercept of the perpendicular line set y=0.
Hence, the x intercept of the perpendicular line is 8.