Answer:
To find the value of x so that line CD is parallel to line EF, you need to determine the slope of each line and make sure they are equal, as parallel lines have the same slope.
The slope of a line passing through points (x1, y1) and (x2, y2) is given by:
Slope = (y2 - y1) / (x2 - x1)
For line CD, you have points C(2, -4) and D(x, 16), so the slope CD is:
Slope_CD = (16 - (-4)) / (x - 2) = (20) / (x - 2)
For line EF, you have points E(-6, 14) and F(-2, 4), so the slope EF is:
Slope_EF = (4 - 14) / (-2 - (-6)) = (-10) / (4)
Now, to make CD parallel to EF, the slopes must be equal, so:
(20) / (x - 2) = (-10) / 4
Now, solve for x:
(20) / (x - 2) = (-10) / 4
Cross-multiply to get:
20 * 4 = -10 * (x - 2)
80 = -10 * (x - 2)
Divide both sides by -10:
-8 = x - 2
Add 2 to both sides:
x = -8 + 2
x = -6
So, the value of x that makes CD parallel to EF is x = -6.