Final answer:
To find the value of x when the slope of a line is -1 and two points are given, we can substitute the values into the slope formula and solve for x = -17
Step-by-step explanation:
To find the value of x, we can use the formula for the slope of a line, which is:
slope = (Y₂ - Y₁) / (X₂ - X₁)
Given that the slope of the line is -1 and the points (2, -9) and (10, x) lie on the same line, we can substitute the values into the formula to solve for x:
-1 = (x - (-9)) / (10 - 2)
By simplifying the equation, we get:
-1 = (x + 9) / 8
Multiplying both sides by 8, we have:
-8 = x + 9
Subtracting 9 from both sides, we find:
x = -17