The problem asks for the correct order of the functions based on their y-intercepts from least to greatest. Let’s examine each function to find their y-intercepts:

Function A:

The equation is given as $y = 2x + 4$. The y-intercept is the constant term in the slope-intercept form $y = mx + b$, which is 4.

Function B:

We need to calculate the equation of the line passing through the points $(-2, -4)$ and $(4, 14)$.

• The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - (-4)}{4 - (-2)} = \frac{18}{6} = 3$
• Using the point-slope form of a line $y - y_1 = m(x - x_1)$, substituting $m = 3$ and $(x_1, y_1) = (-2, -4)$: $y - (-4) = 3(x - (-2))$ $y + 4 = 3(x + 2)$ $y + 4 = 3x + 6$ $y = 3x + 2$ The y-intercept is 2.

Function C:

Looking at the table, the point where $x = 0$ corresponds to the y-intercept, which is 3.

Now, ordering the y-intercepts:

• Function B: y-intercept = 2
• Function C: y-intercept = 3
• Function A: y-intercept = 4

Thus, the order from least to greatest y-intercept is:

$\text{Function B, Function C, Function A}$

The correct answer is:
Option D: Function B, Function C, Function A.

Would you like more details on any of these steps?

Here are 5 questions for further understanding:

1. How do you find the slope of a line between two points?
2. What is the y-intercept, and how can it be determined from a graph or table?
3. How do you use point-slope form to find the equation of a line?
4. What are the key differences between the forms of a linear equation?
5. How does the slope of a line affect its steepness?

Tip: In a linear equation, the y-intercept is where the line crosses the y-axis (when $x = 0$).