Question

What is the equation of a line that is perpendicular to and passes through the point (8, 3)?

Answer 1

@TheSmartOne could i get help with this?

Answer 2

perpendicular to what?

Answer 3

please you have to provide the line of reference

Answer 4

Exactly

Answer 5

sorry didn't realize it wasn't there. its y=4x+5

Answer 6

Good ole algebra, miss those days

Answer 7

hint:
if I call with \(m\) the slope of the refernce line, and with \(m'\) the slope to the perpendicular line to such reference line, then the subsequent condition holds:
\(m \cdot m'=-1\)

Answer 8

reference*

Answer 9

now, I ask what is the slope \(m\) of the line of reference, please?

Answer 10

-1 since they are perpendicular they have the same slope

Answer 11

hint:
what is the slope of this line:
\(y=4x+5\) ?

Answer 12

4 (sorry i got confused xD)

Answer 13

that's right! :)
from my formula above we get:
\[m' = - \frac{1}{m} = ...?\]
please replace \(m=4\), and compute the value of \(m'\). What do you get?

Answer 14

1/4 = 0.25

Answer 15

more precisely it is \(-1/4\), am I right?

Answer 16

yes

Answer 17

ok! Now in order to write the requested equation, we can apply this formula:
\[y - y_0 = - \frac{1}{4}\left( {x - x_0} \right)\]
where \(x_0=8,\;y_0=3\), please replace such values into such equation. What do you get?

Answer 18

y-3=-1/4 (x-8)

Answer 19

that's right!
Now we have to simplify such equation, in order to get an equation of this type:
\(y=mx+q\)
so, I apply the distributive property of multiplication over addition to the right side, and I get:
\[y - 3 = - \frac{x}{4} + 2\]
now, please continue

Answer 20

I don't know what to do from here...

Answer 21

If I add \(3\) to both side, I can write this:
\[y - 3 + 3 = - \frac{x}{4} + 2 + 3\]
please simplify

Answer 22

sides*

Answer 23

hint:
what is \(-3+3=...?\)

Answer 24

@Michele_Laino Youʻre a really good helper ^-^

Answer 25

thanks!! :) :) @ShadowLegendX