Explanation

to get the value for point a
we replace 0 for y in the given equation
this gives 0=1/2 x + 10
-10=1/2 x>>>-20 = x

for b
replace 0 for x to get
y= 10
(B)
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We replace:
(a,0)--> 0=1/2(a)+10; so we get a=-20
(0,b)--> b=1/2(0)+10 we get b=10
b>a

Since the points (a, 0) and (0, b) lie ON the line \(y = \frac{1}{2} x + 10\), we know that the coordinates of those point must satisfy the equation of the line

That is, x = a and y = 0 satisfies the equation \(y = \frac{1}{2} x + 10\)
And x = 0 and y = b satisfies the equation \(y = \frac{1}{2} x + 10\)

Let's test each of these.
(a, 0)
replace x with a and y with 0 to get: \(0 = \frac{1}{2} a + 10\)
Subtract 10 from both sides: \(-10 = \frac{1}{2} a\)
Divide both sides by 1/2 to get: \(-20 = a\)


(0, b)
replace x with 0 and y with b to get: \(b = \frac{1}{2}(0) + 10\)
Simplify: \(b = 10\)

We get:
QUANTITY A: -20
QUANTITY B: 10

Answer: B

Cheers,
Brent
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