Final answer:
To find the equation of a line perpendicular to y = -1/7x + 1 that passes through (-7, -2), first take the negative reciprocal of the original slope to get 7. Then use the point-slope form to plug in the point and the new slope, simplifying it to get the final equation y = 7x + 47.
Step-by-step explanation:
To write an equation of a line that is perpendicular to another line, you need to determine the slope of the original line and then find the negative reciprocal of that slope for the new line. The original line given is y = -1/7x + 1, which means its slope (m) is -1/7. A line perpendicular to this would have a slope of 7 since the negative reciprocal of -1/7 is 7.
Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, plug in the slope of 7 and the point (-7, -2). The equation becomes y - (-2) = 7(x - (-7)).
Simplifying the equation, we get y + 2 = 7x + 49. Subtracting 2 from both sides gives us the final equation of the line: y = 7x + 47.