(-4, 2), perp. to y=x+3

Question

write the equation of the line through the given points perpendicular to the given line

Answer 1

Hi Luke,

 

If you can commit the following equation to memory, you can find the equation of any line:

 

     (y - y₁) = m(x - x₁)       The general expression for a line

 

In the above equation, m is the slope of the line, and (x₁, y₁) are the coordinates of any point on that line.

 

The problem tells us that (-4, 2) is a point on the line, so we know what x₁ and y₁ are. Now all we need to do is to find the slope m.

 

We're told that our line is perpendicular to the line:

 

     y = x + 3      (Eq. 1)

 

What is the slope of this line? Compare Eq. 1 to the general expression for a line. What is m in Eq. 1?

 

     y = 1x + 3

 

Remember that there's a 1 hidden there, as the coefficient of x. So, the slope of this line is 1.

 

Finding the slope of a line that's perpendicular to a line you already know is an easy two-step process.

 

     Step 1: Take the reciprocal of the slope for the line you already know.

     Step 2: Multiply by -1.

 

The reciprocal of 1 is just 1. Multiply by -1, and you'll end up with -1.

 

So, the slope of the line we're trying to find is -1. Now we have everything we need to write the equation of our line:

 

     x₁ = -4,

     y₁ = 2, and

     m = -1.

 

Plug in these values into our general expression for a line:

 

     (y - 2) = -1(x - (-4))

 

Now, get some extra algebra practice in by isolating y by itself on the left-hand side. Good luck!