Final answer:
The equation of the line passing through the point (-13,14) and perpendicular to 4x+9y=5y-5 is y = x + 27, in slope-intercept form.
Step-by-step explanation:
The student is asking for the equation of a line that passes through the point (-13,14) and is perpendicular to another given line. To solve this, first identify the slope of the given line by rearranging the equation 4x + 9y = 5y - 5 into slope-intercept form (y = mx + b).
Rearrange the given equation to 4x + 4y = -5, and then y = -x - 5/4. Here, the slope (m) of the given line is -1. Lines that are perpendicular to each other have slopes that are negative reciprocals, so our new line will have a slope of 1.
Using the point-slope form, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, our equation becomes (y - 14) = 1(x + 13). Simplify to get y = x + 27, which is the equation of the desired line in slope-intercept form, with a slope of 1 and a y-intercept of 27.