Final answer:
The missing coefficient in the equation Ax + 4y = 2 is -82/3, and the missing coefficient in the equation -5x + By = -1 is -21/7.
Step-by-step explanation:
In a linear equation of the form Ax + By = C, -B/A represents the slope of the line. Given the point (3,21) and the equation Ax + 4y = 2, we can substitute the x and y values into the equation to find the missing coefficient. Plugging in 3 for x and 21 for y, we get 3A + 4(21) = 2. Simplifying this equation gives us 3A + 84 = 2. Subtracting 84 from both sides gives us 3A = -82. Dividing both sides by 3, we find that A = -82/3. Therefore, the missing coefficient is -82/3.
Similarly, for the equation -5x + By = -1 and the point (-4,7), we substitute -4 for x and 7 for y, giving us -5(-4) + B(7) = -1. Simplifying this equation gives us 20 + 7B = -1. Subtracting 20 from both sides gives us 7B = -21. Dividing both sides by 7, we find that B = -21/7. Therefore, the missing coefficient is -21/7.