To find the equation of a line perpendicular to 7x - 8y = -3 and passing through the point (-7,5), we need to determine the slope of the given line first.
The slope-intercept form of a line is y = mx + b, where m represents the slope. To find the slope of the given line, we can rearrange the equation into slope-intercept form:
7x - 8y = -3
-8y = -7x - 3
y = (7/8)x + 3/8
The slope of the given line is 7/8.
To find the slope of a line perpendicular to it, we can take the negative reciprocal of 7/8, which is -8/7.
Now that we have the slope (-8/7) and a point (-7,5), we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
y - 5 = (-8/7)(x - (-7))
y - 5 = (-8/7)(x + 7)
y - 5 = (-8/7)x - 8
y = (-8/7)x - 3
Therefore, the equation of the line perpendicular to 7x - 8y = -3 and passing through the point (-7,5) is y = (-8/7)x - 3.