Question

What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?

(y + 2) = −2(x + 5)
(y − 2) = 2(x − 3)
(y − 3) = 2(x − 2)
(y + 3) = −2(x + 2)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values }\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

hmm looks like he has it :~>jdoe can help.

Answer 3

For rise over run I got -4/2 and for point slope I got y-5=-4/2(x+2)
Is this right at all?

Answer 4

Im gonna guess that its D because its the only one with x+2

Answer 5

-4/2 would be run/rise though :)

Answer 6

Than 2/-4 ;D
So than it would be y-5=-2/4(x+2)?

Answer 7

yeap, just bear in mind that \(\bf -\cfrac{\cancel{2}}{\cancel{4}}\iff -\cfrac{1}{2}\)

Answer 8

So then whats next?

Answer 9

hmmm hold the mayo... ... lemme recheck that

Answer 10

ohhh you have a -5....hmm

Answer 11

I put that because of the y1

Answer 12

ok.. then you're correct, is -4/2 which is -2 of course :)
now for the point to use could be either \(x_1,y_1\ or\ x_2,y_2\)

so \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ -5}})\quad
% (c,d)
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies -\cfrac{\cancel{8}}{\cancel{4}}\implies -2
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 3}}={\color{green}{ -2}}(x-{\color{red}{ 2}})\qquad \textit{plug in the values }\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 13

But thats not an answer choice xDDDDD

Answer 14

hmm

Answer 15

Wouldn't it be positive 2 as the rise/run because the negatives both cancel?

Answer 16

ohh yea... darn.. yes it's 3-(-5) = +8
and 2-(-2) = +4

yeap

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ -5}})\quad
% (c,d)
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies \cfrac{\cancel{8}}{\cancel{4}}\implies 2
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 3}}={\color{green}{ 2}}(x-{\color{red}{ 2}})\qquad \textit{plug in the values }\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 17

Thanks for all your help!!