Final answer:
To find the value of n for the points (n, -2) and (9, 7) on a line with a slope of 9/7, you use the slope formula and solve for n, which yields n = 2.
Step-by-step explanation:
The question is asking to find the value of n when the points (n, -2) and (9, 7) fall on a line with a slope of 9/7. To find the value of n, we will use the slope formula, which is (difference in y-coordinates) / (difference in x-coordinates).
To start, we will denote the coordinates as follows: Point 1 (n, -2) and Point 2 (9, 7).
Then, using the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1)
By substituting the given values, we get:
9/7 = (7 - (-2)) / (9 - n)
9/7 = 9 / (9 - n)
To find n, we solve for n by cross-multiplying:
9*(9 - n) = 7*9
81 - 9n = 63
Now, we will isolate n to one side:
-9n = 63 - 81
-9n = -18
Dividing both sides by -9 gives us:
n = 2