Question

the graph of x = 5 is a ____ line with an intercept at ____. choose the correct answer below. a. vertical; (0,5) b. function; (5,0) c. horizontal; (5,0) d. vertical; (5,0)

Explanation:

1. Analyze the equation \(x = 5\): In the coordinate plane, an equation of the form \(x = a\) (where \(a\) is a constant) represents a vertical line. This is because for all values of \(y\), the \(x\)-coordinate remains \(a\). So, \(x = 5\) is a vertical line.
2. Find the intercept: The \(x\)-intercept of a line is the point where the line crosses the \(x\)-axis. On the \(x\)-axis, the \(y\)-coordinate is \(0\). For the line \(x = 5\), when \(y = 0\), \(x = 5\), so the \(x\)-intercept is \((5,0)\). A vertical line \(x = 5\) is not a function (it fails the vertical line test), so option B is incorrect. A horizontal line has an equation of the form \(y = b\), so option C is incorrect. The \(y\)-intercept would be when \(x = 0\), but for \(x = 5\), \(x\) is never \(0\), so the intercept is not \((0,5)\), eliminating option A.

Answer:

D. vertical; \((5,0)\)