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

May 3, 2026Mathematics

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Answer

\text{1}

3 steps

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

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