Final answer:
To find the missing coordinate, substitute the given values into the formula for slope, simplify the equation, and solve for the missing coordinate. The missing coordinate, r, is -19.
Step-by-step explanation:
To find the missing coordinate, we can use the formula for slope:
slope = (change in y-coordinates)/(change in x-coordinates)
Given two points (-1, -9) and (7, ?) on the line with a slope of 5/4, we can substitute these values into the formula:
(-9 - ?)/(7 - (-1)) = 5/4
Simplifying and solving for ?, we get:
-9 - ? = (5/4)(7 - (-1))
-9 - ? = (5/4)(8)
-9 - ? = 10
Now, we can solve for ?, by moving -9 to the right side of the equation:
? = -9 - 10
? = -19
Therefore, the missing coordinate, r, is -19. The correct answer is option C) -19.