Question

write the equation of a line that is parallel to x = 3 and goes through the point (-1,3).

Explanation:

Step1: Analyze the given line

The line \( x = 3 \) is a vertical line (since it has the form \( x = \text{constant} \)). Vertical lines have an undefined slope. Parallel lines have the same slope, so a line parallel to \( x = 3 \) will also be a vertical line.

Step2: Determine the equation of the parallel line

A vertical line passing through the point \( (x_0, y_0) \) has the equation \( x = x_0 \). The given point is \( (-1, 3) \), so the \( x \)-coordinate is \( -1 \). Therefore, the equation of the line parallel to \( x = 3 \) and passing through \( (-1, 3) \) is \( x = -1 \).

Answer:

\( x = -1 \)