Question

Can someone explain or tell me the rules on how to do this? Im trying to find the slope of (-4,5) and (-4,-8), the equation perpendicular through (4,7), the distance from (4,7) to the original line. Im not asking to do my hw because i have to do the same for six more of these. I just dont understand..

Answer 1

use \(y-y_1=m(x-x_1) and the slope formula \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Answer 2

So the slope can be found using the formula \(\large m = \frac{y_2 - y_1}{x_2 - x_1}\)

Answer 3

From that...we can find the equation of the line using the point slope formula *As posted above me*

Answer 4

or the slope intercept formula

Answer 5

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -4}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ -4}}\quad ,&{\color{blue}{ -8}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\)

Answer 6

what's that formula?

Answer 7

Ok, i got that one but finding the equation? I know you have to use what you got from the slope but what next?

Answer 8

Slope intercept is what we are used to seeing in a line

\[\large y = mx + b\]

Answer 9

Basically what you get from simplifying the point slope

Answer 10

\((x_1,y_1)\) (x1,y1) is a point the line passes through

Answer 11

or (x,y) if using slope intercept

Answer 12

my teacher showed me that, he said i have to get b by itself..is m suppose to be the slope?

Answer 13

m will be the slope...but if you need a perpendicular equation, you will need the negative reciprocal slope

Answer 14

what does that mean? Sorry, my teacher didnt explain

Answer 15

for example, if we want a line with a slope of 3 and passes through (6,7)
we plug in our info: \(y-7=3(x-6)\\y-7=3x-18\\y=3x-11\)

Answer 16

reciprocals are "flipped" versions of the original number. \(x \iff \dfrac{1}{x}\)

Answer 17

if you have a slope of lets say 2 (or 2/1)...and you want a perpendicular line...then you need the negative reciprocal slope. That just means " flip " the slope and change the sign. So the negative reciprocal slope of 2/1 is -1/2

Answer 18

ok ok, wait a sec..so would it be 0/13 or 0/-13 since it's already negative

Answer 19

ok...wait...your gonna get this all mixed in your brain...lets start with the first part...finding the slope. You are given 2 sets of points...we will use the slope formula.
slope(m) = (y2 - y1) / (x2 - x1)
set 1 : (-4,5)....x1 = -4 and y1 = 5
set 2 : (-4,-8)....x2 = -4 and y2 = -8
now we sub
slope(m) = (-8 - 5) / (-4 - (-4)
slope(m) = (-13) / (-4 + 4)
slope(m) = -13/0......this means that the slope is undefined...it is a vertical line

Answer 20

Ok, i got that..

Answer 21

little hint : if you are given 2 sets of points...and the x's are the same...it is a vertical line with an undefined slope. If you are given 2 sets of points...and the y's are the same, it is a horizontal line with a slope of 0

Answer 22

the difference between horizontal lines and vertical lines is that the former has 0 slope while the latter has undefined slope.