What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

First we have to find the slope of the givent line and for that we use rise / run method .

The points are (-4,4),(4,-2)

Here rise is

And run is

So slope is

And the slopes of perpendicular lines are negative reciprocal of each other .

Therefore the slope of the required perpendicular line is

Now we use slope intercept form, and put x intercept , that is (6,0) and the slope that is 4/3 ,

Therefore required equation is

Correct option is the third option .