Question

need help I'm stuck-one Q for a dan and a medal

Answer 1

Post away.. :)

Answer 2

can you see the shot?

Answer 3

I just need to be walked through this one /:

Answer 4

so.... what's the slope of say \(\bf y=-\cfrac{1}{5}x-1 ?\)

Answer 5

I need to check if its perp so -1

Answer 6

?

Answer 7

the slope is always -1 in perp lines?

Answer 8

well... nope....

so... what do you think is the slope of AB then?

Answer 9

The slopes of perpendicular lines when multiplied together equal to -1

Answer 10

So the equation you have right now is in the form of y=mx+b where m is the slope.
So now again what is the slope?

Answer 11

-1/5

Answer 12

that would be line A's slope

Answer 13

So \[\frac{ -1 }{ 5 }\times x=-1\]
Solve for x and that will be the slope of the perpendicular line

Answer 14

@MIA305DT What did you get for the slope of the perpendicular line?

Answer 15

one sec

Answer 16

yeap is'd be -1/5

so the slope of an equation perpendicular to that will be the NEGATIVE RECIPROCAL of that

thus \(\bf -\cfrac{1}{{\color{blue}{ 5}}}\qquad negative\implies +\cfrac{1}{{\color{blue}{ 5}}}\qquad reciprocal+\cfrac{{\color{blue}{ 5}}}{1}\)

so, you're really being asked to find the equation of a line whose slope is +5 and that passes through (3, -4)

\(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ -4}})\quad &({\color{red}{ c}}\quad ,&{\color{blue}{ d}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 5
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 17

well... not need for the 2nd point anyhow just \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ -4}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 5
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 18

Or you could plug in (3,4) into y=5x+b and figure out what b is

Answer 19

so -4=5/1(3)-1 am I on the right track here?

Answer 20

Whose way are you doing it?

Answer 21

And I meant (3,-4) previously not (3,4)

Answer 22

idk Im sort of trying the way i learned from school, now i have -4=15-1

Answer 23

on the right track?

Answer 24

Well you should be getting -4=15+b
I am not sure where you got the 1 from...

Answer 25

11 = b?

Answer 26

Actually b=-19

Answer 27

so i don't add -4+15?

Answer 28

-4-15=15-15+b
b=-19

Answer 29

your positive i don't add?

Answer 30

So now that you know what m is and what b is you can put it into slope intercept form which is y=mx+b

Answer 31

Yes I am positive..

Answer 32

y=-1/5x-19?

Answer 33

We can even later test it to make sure it is correct...

Answer 34

No we found out the slope for the perpendicular line is 5...

Answer 35

whoops sorry, y=5x-19?

Answer 36

Exactly..

Answer 37

Now if you want to check it you can graph it.

Answer 38

you are the best ever thank you so much I understand this a lot more

Answer 39

https://www.desmos.com/calculator/5dd2lu113r

Answer 40

The red line is the perpendicular line. You can see it meets at (3,-4) and is perpendicular to the other line.

Answer 41

thank you it was right, thanks again you were a HUGE help

Answer 42

\(\Huge\color{red}{No~Problem~:)}\)