Find the Rate of Change in the Linear Equation 3-y=1/4x

To solve this problem, we'll follow the approach of rewriting the equation in slope-intercept form:

• Step 1: Arrange the equation to isolate $y$.
• Step 2: Identify the coefficient of $x$ as the slope.
• Step 3: Match the slope with the provided choices.

Let's work through these steps:
Step 1: Start with the original equation $3-y=\frac{1}{4}x$. To solve for $y$, add $y$ to both sides:
$3 = \frac{1}{4}x + y$.
Subtract $\frac{1}{4}x$ from both sides to isolate $y$:
$y = -\frac{1}{4}x + 3$.
Step 2: In the equation $y = -\frac{1}{4}x + 3$, the coefficient of $x$ is $-\frac{1}{4}$, which represents the slope or rate of change.
Step 3: Compare the calculated slope $-\frac{1}{4}$ with the given choices. Choice 2, $-\frac{1}{4}$, is correct.

Therefore, the rate of change for the given line equation is $-\frac{1}{4}$.