Question

How do you write the standard form of a line given $( - 2, - 6)$ and slope: undefined?

Answer 1

here in this question slope is undefined, so this is only possible if the line is a vertical line. So the standard form of the line will look like $x = a$, here you just have to find a.

Complete step by step answer:
Standard form of any line is $y = mx + b$
Where m is slope and b is the y-intercept.
The slope of the line when two points on the line are given:
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Here, slope is undefined and this is only possible when${x_2} = {x_1}$.
So, the Standard Form of the line becomes $x = a$.
Now, one point of the line is given,
Which is $( - 2, - 6)$.
So, in this line (slope is undefined) all x-coordinate of the line are the same.

Therefore the standard form of line is $x = - 2$.

Note: There are two special cases of lines:
$1^{st}$ Horizontal lines, in this lines value of y-coordinate is always the same,
So ${y_1} = {y_2}$ and slope of a horizontal line is $0$.
$2^{nd}$ Vertical lines, in this lines values of x- coordinate is always the same,
So ${x_2} = {x_1}$ and slope of a vertical line is undefined.
So this question is based on the $2^{nd}$ special case of line.