Final answer:
To find the equation of a line that is perpendicular to another line, we find the negative reciprocal of the slope of the given line. We can then use the point-slope form of a line to find the equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line is y = -x/6 - 2, so its slope is -1/6. The negative reciprocal of -1/6 is 6/1 or simply 6. Now we have the slope of the line that is perpendicular to the given line.
Next, we can use the point-slope form of a line to find the equation. We are given a point (9,-2), which we can plug into the equation y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Plugging in (9,-2) and the slope 6, we get y - (-2) = 6(x - 9). Simplifying, we have y + 2 = 6x - 54. Subtracting 2 from both sides, we get the equation of the line as y = 6x - 56.