Question

what are the vertical and horizontal intercepts of the horizontal line through the point (-6,5)? select the correct choice below and fill in any answer boxes within your choice. a. the vertical intercept of the line is -6. (type an ordered pair.) b. there is no vertical intercept.

Explanation:

Step1: Recall equation of horizontal line

A horizontal line passing through the point \((-6,5)\) has the equation \(y = 5\).

Step2: Find vertical - intercept

The vertical - intercept is the point where the line crosses the y - axis. For the line \(y = 5\), when \(x = 0\), \(y=5\). The vertical - intercept is the point \((0,5)\). The given answer of \(-6\) for the vertical intercept in option A is incorrect.

Step3: Find horizontal - intercept

The horizontal - intercept is the point where the line crosses the x - axis. Since \(y = 5\) never equals \(0\) (the line is parallel to the x - axis), there is no horizontal intercept.

Answer:

The vertical intercept of the line is \((0,5)\) and there is no horizontal intercept. Since the options only ask about the vertical intercept, the correct choice is not among the given ones. If we assume the question is only about vertical intercept and we correct the option A, the correct answer would be: The vertical intercept of the line is \((0,5)\) (an ordered pair where \(x = 0\) and \(y = 5\)). If we must choose from the given options, both are incorrect as presented. If we consider the concept of vertical intercept for the line \(y = 5\) in a more general sense of the options provided and correct the value in option A, the vertical intercept (ordered pair) is \((0,5)\) and option A with the corrected value would be the answer.