Question

What is the equation of a horizontal line passing through the point ?

a. y=1
b. y=14
c. x=1
d. None of the above

Answer 1

The equation of a horizontal line passing through a point is
`\( \mathbf{y = k} \), where \( k \)` is the y-coordinate of the point. Therefore, the correct option is
`\( \mathbf{b. \ y = 14} \).`

Step-by-step explanation:

For a horizontal line, the equation is of the form
`\( y = k \), where \( k \)` is a constant representing the y-coordinate of any point on the line. In this case, the given options (a)
`\(y=1\) and (c) \(x=1\)` represent vertical lines, not horizontal. Vertical lines have equations of the form
`\(x = h\), where \(h\)` is the x-coordinate of any point on the line.

Option (b)
`\(y=14\)` correctly represents the equation of a horizontal line. It states that, regardless of the x-coordinate, the y-coordinate will always be 14. This is consistent with a horizontal line passing through a point with a y-coordinate of 14.

The option (d) "None of the above" is incorrect, as option (b)
`\(y=14\)`satisfies the criteria for a horizontal line passing through a point. Therefore, the correct answer to the question is option (b),
`\(y=14\)`, providing the accurate equation for a horizontal line passing through the given point.