The value of k is 8
Solution:
Given that, points (9, 9) and (10, k) fall on a line with a slope of -1
To find: value of "k"
The slope of a line with points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here given that,
slope = m = -1
[tex](x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)[/tex]
Substitute the values in formula, and solve to get value of k
[tex]m = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{1}\\\\k-9 = -1\\\\k = -1+9\\\\k = 8[/tex]
Thus the value of k is 8
