The problem shown asks to rewrite the equation $y = \frac{1}{4}x + 3$ by solving for $x$, and then it inquires about which feature of the line can be found using the rearranged equation.

Let's first solve for $x$.

Step 1: Start with the given equation:

$y = \frac{1}{4}x + 3$

Step 2: Subtract 3 from both sides:

$y - 3 = \frac{1}{4}x$

Step 3: Multiply both sides by 4 to isolate $x$:

$4(y - 3) = x$

Thus, the rearranged equation is: $x = 4(y - 3)$

Interpretation:

In this form, $x = 4(y - 3)$, the equation shows the relationship between $x$ and $y$ in terms of $y$. From this, we can find the x-intercept more easily, as setting $y = 0$ will give us the value of $x$ where the line crosses the x-axis.

Would you like a detailed explanation on the process of finding the x-intercept or any other feature of the line? Feel free to ask!

Here are five related questions to deepen understanding:

1. What is the slope of the line in the original equation?
2. How would you find the y-intercept from the original form of the equation?
3. How does changing the slope affect the graph of the line?
4. What happens to the x-intercept if the constant term in the original equation changes?
5. How would you rearrange the equation to express $y$ in terms of $x$ if it were initially given in terms of $x$?

Tip: The slope of a line can tell you how steep it is, while the intercepts give you key points where the line crosses the axes!