Answer:
x = -6
Explanation:
You want the x-coordinate of point X(x, 7) such that line WX is parallel to line UV when the points are U(1, -9), V(5, 7), W(-8, -1).
Graph
It works fairly nicely to graph the given points. This lets you see that line UV has a rise/run of 4/1. You can find the desired point by drawing a line through W with the same slope. It crosses the horizontal line y=7 at x = -6.
The point of interest is X(-6, 7), where x = -6.
Equations
The slope of UV is ...
m = (y2 -y1)/(x2 -x1)
m = (7 -(-9))/(5 -1) = 16/4 = 4
Then the point-slope equation of the line through W is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-1) = 4(x -(-8)
Solving for x gives ...
(y +1)/4 -8 = x
(7 +1)/4 -8 = x = -6 . . . . . . . for point (x, 7)
The x-coordinate of point X is -6.
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