Final answer:
To find the equation of a line perpendicular to y=1/3x and passing through the point (2, -7), we calculate the negative reciprocal of the given slope to find the slope of the perpendicular line, -3. Using the point-slope form, the equation of the required line is y + 7 = -3(x - 2).
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to another line with a given equation, and that passes through a specific point. To find this, we must understand the concept of slope, as illustrated in Figure A1. The slope of a line in the form y = mx + b is represented by m, and for a line to be perpendicular to another, its slope must be the negative reciprocal of the original line's slope.
Given the equation of the other line as y = 1/3 x (omitting the exponent for obvious typo), the slope of our perpendicular line will be -3 (since -3 is the negative reciprocal of 1/3). The point (2, -7) gives us a specific point that our new line must pass through.
Now, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Substituting our values, we get the equation y - (-7) = -3(x - 2), which simplifies to y + 7 = -3(x - 2).