To solve this problem, let's analyze the information provided about the two functions, Function A and Function B.

Step 1: Determine the y-intercept of Function A

Function A is defined by the equation: $y = x + 1$ In this form ($y = mx + b$), the constant term $b$ represents the y-intercept. Here, $b = 1$, so the y-intercept of Function A is $1$.

Step 2: Determine the y-intercept of Function B

For Function B, we have a table of values:

To find the y-intercept, we need the value of $y$ when $x = 0$. We don’t have that directly in the table, so we can calculate the slope (rate of change) between the points to find the equation of Function B.

1. Calculate the slope between two points, say $(-6, -20)$ and $(-3, -8)$: $\text{slope} = \frac{-8 - (-20)}{-3 - (-6)} = \frac{12}{3} = 4$

2. Using the point-slope form, we can write the equation for Function B. Let’s use the point $(-1, 0)$: $y = 4(x + 1)$ Simplifying, we get: $y = 4x + 4$ So, the y-intercept of Function B is $4$.

Step 3: Compare the y-intercepts

• The y-intercept of Function A is $1$.
• The y-intercept of Function B is $4$.

Since $1 < 4$, the correct statement is:

• The y-intercept of Function A is less than the y-intercept of Function B.

Would you like a deeper explanation of any step or have additional questions?

Here are some related questions to further explore this topic:

1. What does the slope of a line tell us about the line’s steepness?
2. How can you determine the slope of a function from a table of values?
3. What does the y-intercept represent in a real-world context?
4. How can you find the equation of a line given two points?
5. What is the importance of understanding linear functions in algebra?

Tip: When comparing linear functions, always check both the slope and the y-intercept, as they provide critical insights into the function's behavior.