Final answer:
After substituting the point (-4, -1) into the equation -(1)/(3)-y=-(13)/(3) and simplifying, it is found that the y-value of the point does not match the y-value from the equation. Hence, the point (-4, -1) does not satisfy the given equation.
Step-by-step explanation:
To determine if the line passing through the point (-4, -1) satisfies the given equation -(1)/(3)-y=-(13)/(3), we should substitute the x and y values of the point into the equation and see if it holds true.
First, we rearrange the equation to solve for y:
-(1)/3 - y = -(13)/3
Add (1)/3 to both sides:
-y = -(13)/3 + (1)/3
-y = -(12)/3
-y = -4
Multiply both sides by -1 to solve for y:
y = 4
Next, we check if the y-coordinate of our point (-1) is equal to the calculated y-value (4):
-1 ≠ 4
Since -1 is not equal to 4, the point (-4, -1) does not satisfy the equation. Therefore, the answer is B. No, it does not satisfy the equation.