Question

position the two points to graph the line x = 1. then enter its characteristics. slope: undefined intercepts: ( ,0) undefined (0, ) undefined

Explanation:

Step1: Recall slope - formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For the line \(x = 1\), all points on this line have \(x\) - coordinate equal to 1. If we consider two points \((1,y_1)\) and \((1,y_2)\) on the line \(x = 1\), then \(x_2-x_1=1 - 1=0\). Since division by zero is undefined, the slope of the line \(x = 1\) is undefined.

Step2: Find \(x\) - intercept

The \(x\) - intercept is the point where the line crosses the \(x\) - axis (\(y = 0\)). For the line \(x = 1\), when \(y = 0\), \(x=1\). So the \(x\) - intercept is \((1,0)\).

Step3: Find \(y\) - intercept

The \(y\) - intercept is the point where the line crosses the \(y\) - axis (\(x = 0\)). But the equation of the line is \(x = 1\), and \(x\) is always 1 and never 0. So the \(y\) - intercept is undefined.

Answer:

slope: undefined
intercepts: \((1,0)\), undefined