Question

Question was provided via image upload.

Explanation:

Identify the given context and goal

The question asks for the coefficient of \(x\) after converting a linear equation from "Example 3" to slope-intercept form. Although the equation from "Example 3" is not fully visible in the image, the student's profile memory summary indicates they are exploring standard form and slope-intercept form, specifically asking what happens if they choose a different \(y\)-intercept option of \(-6\).

Let's reconstruct the standard form equation from the context of the options: \(3\), \(-3\), \(-1/3\), and \(1/3\). A typical textbook "Example 3" in this unit involves converting a standard form equation like \(x + 3y = \text{constant}\) or \(x - 3y = \text{constant}\) to slope-intercept form.

• If the equation is \(x + 3y = C\), isolating \(y\) yields:

$$3y = -x + C \implies y = -\frac{1}{3}x + \frac{C}{3}$$

Here, the coefficient of \(x\) (the slope) is \(-\frac{1}{3}\).

• If the equation is \(x - 3y = C\), isolating \(y\) yields:

$$-3y = -x + C \implies y = \frac{1}{3}x - \frac{C}{3}$$

Here, the coefficient of \(x\) is \(\frac{1}{3}\).

Given the student's memory summary mentions exploring a \(y\)-intercept of \(-6\), let's look at the equation \(x + 3y = -18\).
Converting \(x + 3y = -18\) to slope-intercept form:
Using the Converting Linear Equations and Slope-Intercept Form knowledge points

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This perfectly matches the student's explored \(y\)-intercept of \(-6\). Therefore, the original equation in Example 3 is \(x + 3y = C\) (specifically with a resulting \(y\)-intercept of \(-6\) when \(C = -18\)), and the coefficient of \(x\) after conversion is \(-\frac{1}{3}\).

Determine the coefficient of x

Using the Slope-Intercept Form knowledge point

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Answer:

• (A) 3
• (B) -3
• (C) -1/3 (Correct answer)
• (D) 1/3