Final answer:
The equation of the line perpendicular to y = 14x - 5 through the point (4, -3) is y + 3 = -1/14(x - 4).
Step-by-step explanation:
The given equation is y = 14x - 5. We can determine the slope of this line by comparing it to the standard form of a linear equation, y = mx + b, where m is the slope. In this case, the slope is 14. The line perpendicular to this line will have a slope that is the negative reciprocal of 14. So, the perpendicular line will have a slope of -1/14.
Now, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point. Plugging in the values (4, -3) and the slope -1/14, we get the equation of the line perpendicular to y = 14x - 5 as y + 3 = -1/14(x - 4).