Final answer:
The slope-intercept form of the equation of the line perpendicular to the given line is y = 6.
Step-by-step explanation:
To find the slope-intercept form of the equation of a line perpendicular to a given line, we need to determine the slope of the given line first. The given equation is y + 17 = -7/0(x - 7), which simplifies to y + 17 = 0. This means that the slope of the given line is undefined. Since the line we want to find is perpendicular to the given line, its slope would be the negative reciprocal of the undefined slope, which is 0. To find the equation of the line, we can use the point-slope form y - y1 = m(x - x1). We substitute the point (5,6) and the slope 0 into the equation and simplify to obtain the slope-intercept form of the equation.
Using the point-slope form: y - 6 = 0(x - 5)
Simplifying: y - 6 = 0
Removing the zeroes: y = 6
Therefore, the slope-intercept form of the equation of the line that passes through (5,6) and is perpendicular to y + 17 = -7/0(x - 7) is y = 6.