To find the equation of the linear function $B$ that passes through the points $(1, -4)$ and $(2, 0)$, we need to:

1. Calculate the slope of the line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where $(x_1, y_1) = (1, -4)$ and $(x_2, y_2) = (2, 0)$.

$m = \frac{0 - (-4)}{2 - 1} = \frac{4}{1} = 4$

2. Use the point-slope form of the equation of a line, which is:

$y - y_1 = m(x - x_1)$

Substitute $m = 4$ and the point $(1, -4)$:

$y - (-4) = 4(x - 1)$

Simplifying:

$y + 4 = 4(x - 1)$

$y + 4 = 4x - 4$

$y = 4x - 8$

Thus, the equation of the linear function $B$ is:

$y = 4x - 8$

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Would you like a more detailed breakdown of the steps? Or do you have any other questions?

Here are some related questions to explore:

1. How can you find the slope of a line if only one point and the slope are given?
2. What is the significance of the slope in real-world applications?
3. How do you write the equation of a line in slope-intercept form given two points?
4. What does it mean for a function to be linear?
5. How do you graph a linear equation once you have its equation?

Tip: Always check that the slope makes sense by calculating it using different points if you have the data!