Question

What are the equations of the vertical and horizontal lines that go through the point `(-4,-3)`?

Answer 1

`x+4=0" "`Vertical Line
`y+3=0" "`Horizontal Line

Explanation:

`y=mx+b`

`y=0*x+(-3)`

`y=-3`

`y+3=0" "`Horizontal line

Let us consider two given points on a vertical line

Let `(x_2, y_2)=(-4, 9)` and Let `(x_1, y_1)=(-4, 7)`

Using the Two-Point Form

`y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)`

`(y-y_1)/((y_2-y_1)/(x_2-x_1))=(x-x_1)`

`(y-7)/((9-7)/(-4-(-4)))=(x--4)`

`(y-7)/(oo)=(x--4)`

`0=x+4`

`x+4=0" "`Vertical Line

God bless....I hope the explanation is useful.

Answer 2

vertical is x =- 4
horizontal is y = -3

Explanation:

Vertical lines are parallel to the y-axis and pass through all points in the plane with the same x-coordinate. Since it goes through the point (-4 ,-3) then it will pass through x = -4 , hence the equation of this line is x = -4

Horizontal lines are parallel to the x-axis and pass through all points in the plane with the same y-coordinate. Since it goes through
(-4 ,-3) then it will pass through y = -3. hence the equation of this line is y = -3
graph{(y-0.001x+3)(y-1000x-4000)=0 [-10, 10, -5, 5]}