Question

Choose the slope-intercept equation of the line that passes through the point (-5, -1) and is perpendicular to y = 5 Over 2x + 2.

Answer 1

Perpendicular line given is :

\[y = \frac{5}{2}x + 2\]

Right ??

Answer 2

yes

Answer 3

Can you tell me what is the slope of this line ??

Answer 4

Just compare it with:

\[y = mx + c\]

Answer 5

srry but i dont understand how to do it completly

Answer 6

Just tell the slope..

Compare it with the equation that I have written above.

Simply tell me what is the coefficient of x there ??

Answer 7

srry i just dont know could u work it out with give me an example???

Answer 8

by giving me an example?

Answer 9

Ok I give you one example:

Suppose you have:

\[y = \frac{6}{7}x + 2\]

Compare this equation with:

\[y = mx + c\]

They are just the same equations;

On comparing you get m as ; \(\frac{6}{7}\) and c as 2.

Now can you do the same for :

\[y = \frac{5}{2}x + 2\]
Can you tell what is m here and c here ??

Answer 10

5 over 2x is M and 2 is c

Answer 11

Here m is only 5/2..

Answer 12

ok

Answer 13

This is called slope..

Answer 14

ok

Answer 15

Now one thing you must remember that:

In case of perpendicular lines, if one has slope m then the other line will have the slope of \(\frac{-1}{m}\)..

Answer 16

ok

Answer 17

So, here you got the slope has 5/2.

So the line perpendicular to it will have slope of \(\large \frac{-2}{5}\)..

Getting ??

Answer 18

sorta

Answer 19

I show you..

Answer 20

the only part i dont understand is the -1/m part

Answer 21

\[\large \frac{-1}{m} = \frac{-1}{\frac{5}{2}} \implies \frac{-2}{5}\]

Answer 22

oh ok

Answer 23

so ur the flipping the 5 and 2 and makeing the 2 negative right or is there more to it?

Answer 24

In case of perpendicular lines, their slope product is -1..

\[m_1m_2 = -1\]

Answer 25

ok

Answer 26

From here:
\(m_1 = \frac{5}{2}\)

So, you will get \(m_2 = \frac{-2}{5}\)

Answer 27

ok

Answer 28

So now you have slope and one point is also given to you:

The required equation is given by:

\[\large y - y_1 = m(x - x_1)\]

Here:

\[x_1 = -5, y_1 = -\]
\[m = \frac{-2}{5}\]

Just plug in the values and find the equation..

Answer 29

\[y_1 = -1\]

Answer 30

im lost now :PP

Answer 31

I give you one example:

Suppose the points given will be: \((-4, -5)\)

And the slope is \(\frac{-7}{6}\)

So according to that equation:

\[y - y_1 = m(x - x_1)\]
\[y - (-5) = \frac{-7}{6}(x - (-4))\]

\[y + 5 = \frac{-7}{6}(x +4)\]

\[6y + 30 = -7x - 28\]

Do the same above..

Answer 32

would it be y = -2/5x-3?