Final answer:
To find the value of s for the line with a slope of -1/5 passing through points (s, -10) and (-2,-8), we use the slope formula. After setting up the equation 2 / (-2 - s) = -1/5 and simplifying, we determine that s equals -1.6.
Step-by-step explanation:
The question asks to find the value of s when a line passing through the points (s, -10) and (-2,-8) has a slope of -1/5. The slope of a line through two points (x1, y1) and (x2, y2) is calculated as (y2 - y1) / (x2 - x1). In this case, we know the slope (-1/5), and one set of x and y values, which allows us to set up an equation and solve for s.
Let's use the points (s, -10) and (-2, -8) with the given slope of -1/5:
(-8 - (-10)) / (-2 - s) = -1/5
Simplifying this equation, we get:
2 / (-2 - s) = -1/5
To find the value of s, we multiply both sides by (-2 - s) and then by -1/5 to isolate s:
-2 - s = -2/5
s = -2 + 2/5
s = -10/5 + 2/5
s = -8/5 or -1.6