Answer: s= -8
Step-by-step explanation:
The gradient of the ski slope can ge used as the slope (literally) of a line equation:
y = mx + b,
where m is the slope and b the y-intercept (the value of y when x = 0).
The first slope would be y = -(1/3)x + b.
The slope is (-1/3) since the ski run is headed downhill. The second ski slope is assumed to have the same gradient ("two parallel straight ski slopes").
y' = -(1/3)x' + b
We may assume that b is the same for both slopes - they start and end at the same point.
We can find b by using the given point (2,-3):
y' = -(1/3)x' + b
-3 = -(1/3)(2) + b
-3 = -(2/3) + b [Add -(2/3) to both sides: (-3 + 2/3 = -9/3 + 2/3 = -7/3]
-7/3 = b
b = -(7/3)
The second ski slope, y', thus has the equation
y' = (1/3)x' -(7/3)
We want the value of s in (s, -5).
y' = (1/3)x' -(7/3)
-5 = (1/3)s -(7/3)
(1/3)s = -5 +(7/3) [-15/3 + 7/3 = -8/3]
(1/3)s = -(8/3) [Multiply both dies by 3]
s = -(24/3)
s = -8
