Question

Write the slope-intercept form of the equation through (-5, -4) perpendicular to y=5x+1

Answer 1

Ah! This brings me back to Coordinate Geometry!

Explanation:

First, we need to find the slope of our line. We can't do this using the single point we are given, so we are going to have to use the other line for reference.

Now, if you did not know, the equation to find the slope of one line perpendicular to another line is:

`m_(1) =-(1)/(m_(2) )`

Where m1 is the slope of one line, and m2 is the slope of the other.

So, we input it!

`m_(1) =-(1)/(5)`

See? Easy! (m1 is the slope of the line we are trying to find)

Thus,

`y=-(1)/(5)x+b\\`

Gotta go!

Then we input the point into this equation to find the y-intercept!

Thus,

`y=-(1)/(5)x+b\\\\-4=1+b\\-5=b`

So there's your line:
`y=-(1)/(5) x-5`

Hope this helps!

Gotta Go!

P.S. Stay Safe!