Which of these is a point-slope equation of the line that is perpendicular toy – 3 = 4(x – 10) and passes through (–3, 7)?A.y – 7 = –1441​ (x + 3)B.y + 7 = 4(x – 3)C.y + 7 = –1441​ (x – 3)D.y – 7 = –4(x + 3)SUBMITarrow_backPREVIOUS

The equation of the line given is in point-slope form, y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

The slope of the given line is 4. The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.

The point through which the perpendicular line passes is (-3, 7).

Substituting these values into the point-slope form of the equation gives:

y - 7 = -1/4(x + 3)

Multiplying through by 4 to get rid of the fraction gives:

4(y - 7) = -(x + 3)

This simplifies to:

4y - 28 = -x - 3

Rearranging terms gives:

4y = x + 31

This is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7).

However, none of the given options match this equation. There may be a mistake in the question or the answer choices.