Step-by-Step Explanation

Find the equation of line k :
Line k has a slope m=3 and passes through the point $(a, b)$. Using the point-slope form:


y-b=3(x-a)
y=3 x-3 a+b


Substitute b=2 a+10 into the equation:


y=3 x-3 a+(2 a+10)
y=3 x-a+10


Identify the \(\boldsymbol{y}\) -intercept (Quantity A):
The y -intercept occurs where x=0 :


\(\text { Quantity } \mathrm{A}=10-a\)


4. Compare Quantity A and Quantity B:

Quantity A: 10-a
Quantity B: 10

The relationship between $10-a$ and 10 depends entirely on the sign/value of a :

If a>0 (e.g., a=2 ), then Quantity \(\mathrm{A}=8\) , which is less than Quantity B.
If a=0 , then Quantity \(\mathrm{A}=10\) , which is equal to Quantity B.
If a<0 (e.g., a=-2 ), then Quantity \(\mathrm{A}=12\) , which is greater than Quantity B.

Since the exact value of \(a\) is unknown, the relationship cannot be uniquely determined.

Correct Answer
D. The relationship cannot be determined from the information given.