Question

Write the equation of a vertical line that passes through the point (3, -3)

Answer 1

hello
the equation of a vertical line that passes through the point (3, -3) is : x = 3

Answer 2

The equation of a vertical line that passes through the point
`(3,-3)` is

`x=3`

Explanation:

The equation of a generic line is :

`y=ax+b` (I)

Where ''a'' and ''b'' are real numbers.

The horizontal and vertical lines are particular cases of the equation (I).

If ''x'' is equal to 0 ⇒

`y=a.(0)+b\\y=b`

Where ''b'' is still a real number. The equation
`y=b` gives us the family of all horizontal lines which cut the y-axis in the point
`(0,b)`

Now, if ''y'' is equal to 0 ⇒

`0=ax+b`

`ax=-b`

`x=(-b)/(a)`

If we replace ''
`(-b)/(a)`'' by ''c'' (where ''c'' is a real number), the equation
`x=c` gives us the family of all vertical lines which cut the x-axis in the point
`(c,0)`.

If we want to write the equation of a vertical line we can write

`x=c` and then we will need to find the value of ''c''. Our line must passes through the point (3,-3). If the second coordinate is 0 then the vertical line will intersect the x-axis at
`(3,0)` ⇒ It equation will be
`x=3`