SOLUTION: Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y=6x+1. A perpendicular brace passes through the point (-4, 6). Write an equation of th

 

The red line is the line whose equation is 

y = 6x + 1

We compare that to

y = mx + b

and see that the slope = m = 6. [b=1 means the y-intercept is 
(0,1) but we don't need that for this problem]

The green line is what we want the equation of

Since the green line is perpendicular to the red
line, its slope is the negative reciprocal of
the slope of the red.  That's 1 over 6 with the
sign changed to negative, or .  And
the green line goes through (-4,6).  So we use
the point slope formula:

y - y1 = m(x - x1)

  y - 6 = [x - (-4)]

  y - 6 = (x + 4)

That's the equation in point-slope form.

If we want it in general equation, we multiply through
by 6

6y - 36 = -1(x + 4)

6y - 36 = -x - 4

 x + 6y = 32

If you want the slope-intercept form, solve it for y:

     6y = -x + 32

     6y = -1x + 32

Divide through by 6

     = x + 

      y = x + 

Edwin