Final answer:
The equation of the line perpendicular to 5x - 4y = 7 and passing through the point (-15,8) is y = (-4/5)x - 4.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line and passes through the given point (-15,8), we need to determine the slope of the original line and then find the perpendicular slope. The original equation is 5x - 4y = 7, which can be written in slope-intercept form as y = (5/4)x - (7/4). Hence, the slope of this line is 5/4. The perpendicular slope will be the negative reciprocal of 5/4, which is -4/5.
Now, using the point-slope form of a line's equation, y - y1 = m(x - x1), where m is the perpendicular slope and (x1, y1) is the given point (-15, 8), we have:
y - 8 = (-4/5)(x + 15)
Expanding and simplifying, we get:
y = (-4/5)x - (4/5)(15) + 8
y = (-4/5)x - 12 + 8
y = (-4/5)x - 4
Thus, the equation of the perpendicular line in slope-intercept form is y = (-4/5)x - 4.