Final answer:
To find the equation of a line perpendicular to x=-2 and passing through (3,6), we determine that it must be a horizontal line and therefore has the form y=k. Since it passes through the point (3,6), the equation is y=6.
Step-by-step explanation:
The question asks to find the equation of a line that is perpendicular to a given line which has the equation x=-2, and which passes through the point (3,6). Given that x=-2 is a vertical line, any line that is perpendicular to it must be a horizontal line. The equation of a horizontal line does not vary with x, meaning that it has the form y=k where k is the y-coordinate of any point through which it passes.
Since the line must pass through the point (3,6), we immediately know that the equation of our line is y=6. This line is horizontal and will cross the y-axis at 6, and it will be perpendicular to the vertical line x=-2 as required.