Final answer:
The slope-intercept form for a line perpendicular to x=4 and passing through (-6, 5) is y=5, as it has a slope of 0. For a line perpendicular to y=6 through the same point, the equation is x=-6, since perpendicular lines to horizontal lines are vertical and do not have a defined slope.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. A line that is perpendicular to another has a slope that is the negative reciprocal of the original line's slope.
(a) The equation x = 4 represents a vertical line, so a line perpendicular to it would be a horizontal line, which has a slope of 0. Therefore, the slope-intercept form of the line through (-6, 5) and perpendicular to x = 4 would be y = 5.
(b) The equation y = 6 represents a horizontal line, so a line perpendicular to it would be a vertical line, which does not have a slope in the traditional sense (it is undefined). However, the equation of a vertical line can be expressed as x = h, where h is the x-coordinate of all points on the line. Since our line passes through (-6, 5), the equation is x = -6.