Let's examine the problem step-by-step.

Information provided:

1. Function A: $y = x + 4$ This is a linear equation with a slope of $1$ and a y-intercept of $4$.

2. Function B: Given data points:

   • When $x = -5$, $y = -18$
   • When $x = -3$, $y = -10$
   • When $x = 3$, $y = 14$

Finding the Equation of Function B

To determine the equation of Function B, follow these steps:

1. Calculate the slope ($m$) using two points. Let's use $(-5, -18)$ and $(-3, -10)$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - (-18)}{-3 - (-5)} = \frac{8}{2} = 4$

2. The slope ($m$) is $4$. Now, use the slope-intercept form $y = mx + b$ to find the y-intercept ($b$).

   • Use point $(-3, -10)$: $-10 = 4(-3) + b$ $-10 = -12 + b$ $b = 2$

So, the equation for Function B is: $y = 4x + 2$

Comparing y-Intercepts

• Function A has a y-intercept of $4$.
• Function B has a y-intercept of $2$.

Conclusion:

The y-intercept of Function A is greater than the y-intercept of Function B. Thus, the correct answer is:

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

Would you like a deeper explanation or have any further questions?

Related Questions:

1. How do you calculate the slope between two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do you determine if two linear functions are parallel or intersecting?
4. What is the general form of a linear equation and how do you convert it to slope-intercept form?
5. How can you predict the behavior of a line based on its slope and y-intercept?

Tip:

When comparing linear functions, the y-intercept tells you where each line crosses the y-axis. A higher y-intercept indicates the line crosses the y-axis at a higher point.