Final answer:
The value of w is -13 to achieve the desired slope between the two points, and the value of x to maintain a slope of 14 through the given points is 3.
Step-by-step explanation:
To find w so that the slope of the line through (w, -8) and (-3, 5) is -13/10, we use the slope formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
-13/10 = (5 - (-8)) / (-3 - w)
-13/10 = 13 / (-3 - w)
Multiplying both sides by (-3 - w) and -10, we arrive at:
130 = 13(-3 - w)
10 = -3 - w
Thus, w = -13.
To find x so that the line with a slope of 14 contains the points (x, -20) and (3x - 4, 8), we again use the slope formula:
14 = (8 - (-20)) / ((3x - 4) - x)
14 = 28 / (2x - 4)
Multiplying both sides by (2x - 4), we find:
14(2x - 4) = 28
28x - 56 = 28
x = 3