Final answer:
To find a line perpendicular to y = 5x - 10 and passing through (-10, 12), we can find the negative reciprocal of the slope of the given line and use the point-slope form of a linear equation.
Step-by-step explanation:
To determine which line is perpendicular to y = 5x - 10 and passes through the point (-10, 12), we need to find the negative reciprocal of the slope of the given line. The slope of y = 5x - 10 is 5, so the negative reciprocal of 5 is -1/5. We can then use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values (-10, 12) and -1/5 for m, we can calculate the equation of the line:
y - 12 = -1/5(x - (-10))
y - 12 = -1/5(x + 10)
y - 12 = -1/5x - 2
y = -1/5x + 10
Therefore, the line that is perpendicular to y = 5x - 10 and passes through the point (-10, 12) is y = -1/5x + 10. None of the given options match this equation, so the answer is none of the above.