Final answer:
The equation of the line perpendicular to y = 7/3 x + 10 that passes through (-1, 1) is y = -3/7x + 5/7.
Step-by-step explanation:
The equation of the line that is perpendicular to y = 7/3 x + 10 and passes through the point (-1, 1) can be found by first determining the slope of the perpendicular line. A line perpendicular to another has a slope that is the negative reciprocal of the original line's slope.
The slope of the given line is ·7/3, so the slope of the perpendicular line is -3/7. With the slope and a point (-1, 1), we use the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Substituting the values, we get y - 1 = -3/7(x + 1). Simplifying this equation, we get the final equation of the perpendicular line: y = -3/7x - 2/7 + 1, which simplifies to y = -3/7x + 5/7.