Hey I know this is a bit much but I’m really confused.

Question

Given the line y=5, write the equation of the line that passes through (3,-6).

The line y=5 is a (__) on a graph, so the line that is perpendicular will be (__) on the graph.

The line y=5 has a slope of (__), and the line that is perpendicular has a slope of (__).

The equation for the perpendicular line is (__).

Answer 1

Graphically, y=5 is a flat horizontal line, with y intercept (0,5).

A line perpendicular to y=5 is a vertical line.

y=5 has slope = 0

a perpendicular line, perpendicular to y=5 has an undefined slope (or you could say infinity or negative infinity) It's a vertical line which has no defined slope. It approaches in the limit a slope of infinity or -infinity.

a line perpendicular to y=5 that goes through the point (3,-6) is x=3, it's a vertical line with undefined slope.

If you're asking for a parallel line, parallel to y=5, that goes through (3,-6), it doesn't exist. No solution.