Question

1. function a
2. function b

$y = \frac{1}{3}x$
which statement is true?
the y-intercept of function a is greater than the y-intercept of function b.
the y-intercept of function a is less than the y-intercept of function b.

Explanation:

Step1: Find y-intercept of Function A

The graph crosses the y-axis at $(0,0)$, so the y-intercept is $0$.

Step2: Find y-intercept of Function B

For $y=\frac{1}{3}x$, substitute $x=0$:
$y=\frac{1}{3}(0)=0$, so the y-intercept is $0$.

Step3: Compare the two y-intercepts

Both y-intercepts are equal, so the statement "The y-intercept of Function A is less than the y-intercept of Function B" is false, and "The y-intercept of Function A is greater than the y-intercept of Function B" is also false. However, re-evaluating, since both intercepts are $0$, the correct conclusion is that neither statement is true, but based on the options, the second option (less than) is incorrect, and the first (greater than) is incorrect. Wait, correction: both intercepts are $0$, so they are equal. But since we must choose from the given options, we confirm:
Function A y-intercept: $0$
Function B y-intercept: $0$
So $0$ is not greater than $0$, and $0$ is not less than $0$. But if forced to assess the given statements, both are false, but rechecking the graph: the line passes through $(0,0)$, correct. Function B is $y=\frac{1}{3}x$, which has y-intercept $0$.

Answer:

Neither statement is true, but if evaluating the given options:

• "The y-intercept of Function A is greater than the y-intercept of Function B": False
• "The y-intercept of Function A is less than the y-intercept of Function B": False

The actual correct fact is that the y-intercepts of Function A and Function B are equal (both $0$).