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 a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. But for the line $x = 1$, all points on this line have $x$-coordinate equal to 1. The line is vertical. For a vertical line, the denominator in the slope - formula is 0. So the slope is undefined.

Step2: Find $x$-intercept

The equation of the line is $x = 1$. To find the $x$-intercept, we set $y = 0$. Substituting $y = 0$ into the equation $x = 1$, we get the point $(1,0)$.

Step3: Find $y$-intercept

To find the $y$-intercept, we set $x = 0$. But the equation of the line is $x = 1$, and there is no value of $y$ for which $x = 0$. So the $y$-intercept is undefined.

Answer:

slope: undefined
$x$-intercept: $(1,0)$
$y$-intercept: undefined