Question

2. Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2.

Answer 1

How would you write it in standard form?

Answer 2

\(\Huge{\color{purple}{\textbf{W}} \color{orange}{\cal{E}} \color{green}{\mathbb{L}} \color{blue}{\mathsf{C}} \color{maroon}{\rm{O}} \color{red}{\tt{M}} \color{gold}{\tt{E}} \space \color{orchid}{\mathbf{T}} \color{Navy}{\mathsf{O}} \space \color{OrangeRed}{\boldsymbol{O}} \color{Olive}{\mathbf{P}} \color{Lime}{\textbf{E}} \color{DarkOrchid}{\mathsf{N}} \color{Tan}{\mathtt{S}} \color{magenta}{\mathbb{T}} \color{goldenrod}{\mathsf{U}} \color{ForestGreen}{\textbf{D}} \color{Salmon}{\mathsf{Y}} \ddot \smile }\)

The line is perpendicular, meaning it'll have the opposite slope.

We are given the two points: (2, 1)

Along with the equation: x = -2

Slope: 2
Points: (2, 1)

Now yo want to plug it into the formula: \[y - y1 = m(x - x1)\]
Where: x1 = 2
y1 = 1
And m = 2

Answer 3

@Compassionate won't the slope of the line be 1/2??

Answer 4

2 is the same as 1/2

Answer 5

Yeah, I got 1/2 as the slope but I got it wrong so now I'm fixing it

Answer 6

1/2 ?
2 ?

Guys, the slope of the line x = -2 (this is a vertical line) is undefined, meaning, for a line to be perpendicular to this, the line should have a slope 0...

Answer 7

oh okay.....
sorry for the mistake then..

Answer 8

So, we're looking for a horizontal line which passes through the point (2,1)

Answer 9

Pardon me, but the slope is zero for any vertical line.

Answer 10

Uhh, no, vertical lines don't have a slope zero, they have an undefined slope, an infinite slope, if you will...

Answer 11

Compassionate, vertical lines have an undefined slope because:
\[m = \frac{dy}{dx}\]
So if the change in y is large and the change in x is small then we have an indeterminate quantity.

Horizontal lines have a slope of 0 because delta y is zero for any finite delta x.