Final answer:
A line parallel to 3x - 2y = 14 must have the same slope, which is 3/2. Using the point (-6, -1), we calculate the y-intercept, which turns out to be 8. Thus, the correct equation is y = (3/2)x + 8, although it is not listed in the given choices.
Step-by-step explanation:
To find an equation that is parallel to a given line and passes through a specific point, we need to ensure that the new line has the same slope as the original line. The general form of a linear equation is y = mx + b, where m is the slope, and b is the y-intercept. For the given equation, 3x – 2y = 14, we first need to solve for y to find the slope.
Re-writing the equation in slope-intercept form gives us:
3x – 2y = 14
-2y = -3x + 14
y = (3/2)x - 7
So, the slope (m) of the line is 3/2. Since parallel lines have the same slope, the slope of the line we are looking for will also be 3/2.
Next, we'll use the point (-6, -1) to find the b (y-intercept) for our new line:
y = mx + b
-1 = (3/2)(-6) + b
-1 = -9 + b
b = 8
Thus, the equation of the line that is parallel to 3x – 2y = 14 and passes through (-6, -1) is y = (3/2)x + 8. However, this option is not present among the given choices, indicating a potential typo or error in the choices provided.