Final answer:
To find the value of r, use the slope of the line that passes through the points (3, r) and (r, -1) and solve the equation (-1-r)/(r-3) = -3/4.
Step-by-step explanation:
To find the value of r, we can use the slope of the line that passes through the points (3, r) and (r, -1). The slope of a line is given by the formula: slope = (change in y)/(change in x). We are given that the slope is -3/4, so we can set up the equation (-1-r)/(r-3) = -3/4. Now, we can solve this equation to find the value of r.
First, let's cross multiply to get rid of the fractions: -4(-1-r) = -3(r-3). Simplifying this, we get 4+4r = -3r+9. Combining like terms, we get 7r = 5. Dividing both sides by 7, we find that r = 5/7.