Calculate the slope of the line using the two given points (4, 2) and (-8, -2).

Morning Bright — let's get this done.

Step 1: Calculate the slope of the line using the two given points $(4, 2)$ and $(-8, -2)$. The formula for the slope $m$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$. $m = \frac{-2 - 2}{-8 - 4}$ $m = \frac{-4}{-12}$ $m = \frac{1}{3}$

Step 2: Rewrite the given equation of the line $3y = px + q$ into the slope-intercept form $y = mx + c$. Divide the entire equation by 3: $y = \frac{p}{3}x + \frac{q}{3}$ From this form, the slope of the line is $m = \frac{p}{3}$.

Step 3: Equate the slope calculated from the points to the slope from the equation and solve for $p$. $\frac{p}{3} = \frac{1}{3}$ Multiply both sides by 3: $p = 1$

The value of $p$ is 1. This corresponds to option (a).

The final answer is $\boxed{1}$. Send me the next one 📸