Write an equation of the line with the given properties. Your answer should be written in standard form.

m is undefined passing through P(−7, −9)

"m is undefined" implies that the line is vertical

The equation of a vertical line takes the form x = k, where k is the x value of any point on the line, so ....
x = -7

standard form : x + 0y = -7 if you insist

Well, the equation of a line with an undefined slope is a vertical line. And since it passes through the point P(-7, -9), we know that the x-coordinate of every point on the line will be -7.

So we can say that the equation of the line is x = -7.

But wait, x = -7 is already in standard form! So there you have it, the equation of the line is x = -7. It's as straightforward as a vertical line can be!

To find the equation of a line with an undefined slope passing through a point P(-7, -9), we know that the line is vertical, going straight up and down.

Since the slope is undefined, we cannot use the slope-intercept form of a linear equation (y = mx + b) because there is no value for 'm'. Instead, we will use the standard form of a linear equation, which is Ax + By = C.

For a vertical line passing through the point P(-7, -9), the x-coordinate remains constant while the y-coordinate can vary. Therefore, the equation of the line can be written as x = -7.

Rewriting this equation in standard form by moving the x term to the left side, we get:

x - 0y = -7

Simplifying, the equation becomes:

x = -7

So, the equation of the line passing through P(-7, -9) with an undefined slope is x = -7 in standard form.

To write the equation of a line in standard form, we need to use the slope-intercept form (y = mx + b) and manipulate the equation to express it in the form Ax + By = C, where A, B, and C are integers.

Given that the slope (m) is undefined, we know that the line is vertical. A vertical line does not have a defined slope because the change in x is always 0, resulting in division by zero. Therefore, a vertical line takes the form x = a, where 'a' is a constant representing the x-coordinate at any point on the line.

Since the line passes through P(-7, -9), the x-coordinate of all the points on this line will be -7. Therefore, our equation becomes:

x = -7

To express this equation in standard form, we need to manipulate it further. We can rewrite it as:

x + 0y = -7

Notice that we introduced the term 0y, which is to account for the absence of a y-variable in the equation. The equation x = -7 is now in the form Ax + By = C, with A = 1, B = 0, and C = -7.

Therefore, the equation of the line passing through P(-7, -9), with an undefined slope, in standard form is:

1x + 0y = -7