Final answer:
The correct point-slope form equation of the line passing through the points (3, 4) and (-3, -8) is y - 4 = 2(x - 3). The calculation involves finding the slope and then using the point-slope form equation with one of the given points.
Step-by-step explanation:
To find the equation of the line in point-slope form that passes through the points (3, 4) and (-3, -8), we first need to calculate the slope of the line. The slope (m) is found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Substituting the values from the points gives us:
m = (-8 - 4) / (-3 - 3) = (-12) / (-6) = 2.
Now, using one of the points, say (3, 4), and the slope, the point-slope form equation is written as:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting the values into the point-slope form gives us:
y - 4 = 2(x - 3).
Therefore, the correct point-slope form equation for the line passing through the given points is y - 4 = 2(x - 3). None of the options provided (A, B, C, or D) match this equation exactly, so there may be an error in the question or the response options.