Question

find the slope and the y - intercept of the line. x = - 2 select the correct choice below and fill in any answer boxes in your choice. a. the slope is (simplify your answer. type an integer or a fraction.) b. the slope is undefined. select the correct choice below and fill in any answer boxes in your choice. a. the y - intercept is (simplify your answer. type an ordered pair. use integers or fractions for any numbers in the expression.) b. there is no y - intercept.

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the line $x=-2$, all points on this line have $x -$coordinate equal to $-2$. If we take two points $( - 2,y_1)$ and $(-2,y_2)$ on the line, then $x_1=x_2=-2$. Substituting into the slope formula gives $m=\frac{y_2 - y_1}{-2-(-2)}=\frac{y_2 - y_1}{0}$, which is undefined.

Step2: Recall y - intercept definition

The y - intercept is the point where the line crosses the y - axis. The equation of the y - axis is $x = 0$. The line $x=-2$ is a vertical line parallel to the y - axis and never crosses it. So, there is no y - intercept.

Answer:

B. The slope is undefined.
B. There is no y - intercept.