Final answer:
To find the missing coordinate r for the point (-3, r) on a line with a given slope of -5/4, we use the slope formula with the given points (-3, r) and (-5, 5), leading to the conclusion that r = 10.
Step-by-step explanation:
The question asks us to find the missing coordinate r for the point ℃3, r) that lies on a line with a known slope and another given point. Using the slope formula, (y2 - y1)/(x2 - x1), we set up the equation with the known slope of 3'5/4) and points ℃3, r) and 3'5, 5).
Applying the known values, we use the equation:
3'5/4) = (r - 5)/(–3 + 5)
Solving this equation, we'd find the value of r. First, we multiply both sides by the denominator on the right side to get rid of the fraction:
'4 * '5/4) = (r - 5)
Then, simplifying:
'5 = r - 5
Adding 5 to both sides, we find that:
r = 10
Therefore, the missing coordinate r is 10.