Final answer:
The slope-intercept equation for a line perpendicular to the vertical line x=-3, passing through the point (5,-5), is y = -5. This is because a line perpendicular to a vertical line is horizontal, which means its slope is 0 and the y-value is constant.
Step-by-step explanation:
To write a slope-intercept equation for a line that is perpendicular to another line, we first need to determine the slope of the original line. Since we are given that the original line is x=-3, we can infer it is a vertical line, which has an undefined slope. A line that is perpendicular to a vertical line is a horizontal line, which has a slope of 0.
Since the slope (m) is 0 for a horizontal line, no matter what x-value we have, the y-value will stay constant. As the line passes through the point (5,-5), the y-value will always be -5, hence the y-intercept (b) is -5. Therefore, the slope-intercept equation of the line perpendicular to x=-3, passing through the point (5,-5) is y = -5.