Final answer:
The equation of the line parallel to the given line y = -3/2x + 6 that passes through the point C(6, -2) is y = -3/2x + 7.
Step-by-step explanation:
To write an equation of a line parallel to the given line y = -3/2x + 6 that contains the point C(6, -2), we should use the same slope since parallel lines have equal slopes.
The slope of the given line is -3/2. Therefore, the slope of the parallel line we are looking for will also be -3/2.
Now we can apply the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging the slope -3/2 and the point (6, -2) into the point-slope form, we get:
y + 2 = -3/2(x - 6)
Simplifying this equation will give us the final equation of the parallel line:
y + 2 = -3/2x + 9
Finally, subtracting 2 from both sides, we have the equation of the parallel line:
y = -3/2x + 7