Question

what are the vertical and horizontal intercepts of the vertical line through the point (-3,7)? select the correct choice below and fill in any answer boxes within your choice. a. the vertical intercept of the line is (type an ordered pair.) b. there is no vertical intercept.

Explanation:

Step1: Recall the equation of a vertical line

A vertical line passing through the point \((-3,7)\) has the equation \(x = - 3\). The vertical - intercept is the point where the line crosses the \(y\) - axis, i.e., the point where \(x = 0\). Since the equation of the line is \(x=-3\) and \(x\) is always \(-3\) for all points on this line, it never crosses the \(y\) - axis.

Step2: Recall the horizontal - intercept

The horizontal - intercept is the point where the line crosses the \(x\) - axis. For the line \(x=-3\), when \(y = 0\), \(x=-3\). So the horizontal intercept is \((-3,0)\). But we are only asked about the vertical intercept here.

Answer:

B. There is no vertical intercept.