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Answer:
y = -3/4(x -2)
Step-by-step explanation:
You are given point (2, 0) on the new pipeline. To find the equation of it, you need to know the slope of the line on the graph. A careful look at the graph shows you the line goes through grid points that are separated by 4 units horizontally, and 3 units vertically. For a positive horizontal change, the vertical change is negative, so the slope is ...
m = rise/run = -3/4
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For m = -3/4 and (h, k) = (2, 0), the equation is ...
y = -3/4(x -2)
_____
Additional comments
If you use the distributive property to eliminate parentheses, the equation becomes ...
y = -3/4x +3/2
The slope of the red pipeline can also be determined by considering the slope of the blue pipeline. The two marked points on that line have a horizontal separation of 3 and a vertical separation of 4. Its slope is ...
m = rise/run = 4/3
The slope of the perpendicular (red) line is the opposite reciprocal of this:
-1/m = -1/(4/3) = -3/4 . . . . as we determined from the red line's graph
