Final answer:
To find the value of r, we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept. Using the given slope and two points on the line, we can set up two equations and solve for r.
Step-by-step explanation:
To find the value of r, we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept. We have the slope m = -3 and two points on the line, (-9, 3) and (7, r).
Using the slope-intercept form, we can write two equations:
1. 3 = -3(-9) + b (using the first point)
2. r = -3(7) + b (using the second point)
Simplifying these equations, we get:
1. 3 = 27 + b
2. r = -21 + b
From equation 1, we can solve for b by subtracting 27 from both sides:
b = -24
Substituting b = -24 into equation 2, we can solve for r by adding 21 to both sides:
r = -21
Therefore, the value of r is -21.