Question

What is the equation of the line that passes through the point (3, -4) and is parallel to y−71=−78(x−1)?

A. y+4=−78(x−3)
B. y+4=78(x−3)
C. y−4=−78(x−3)
D. y−4=78(x−3)

Answer 1

The equation of the line that passes through the point (3, -4) and is parallel to the given line y - 71 = -7/8(x - 1) is y + 4 = -7/8(x - 3), which is option A.

Step-by-step explanation:

To find the equation of a line that is parallel to another line and passes through a given point, we need to use the fact that parallel lines have the same slope. The given line y - 71 = -7/8(x - 1) has a slope of -7/8. To write the equation of a line parallel to this one and that passes through the point (3, -4), we use the point-slope formula which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.

Substituting the known values into the point-slope formula, we get y - (-4) = -7/8(x - 3), which simplifies to y + 4 = -7/8(x - 3). This matches choice A from the given options.