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)

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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)

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\(\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({\color{red}{ -2}}\quad ,&{\color{blue}{ 5}})\quad % (c,d) &({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}}) \end{array} \\\quad \\ % slope = m slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}} \\ \quad \\ % point-slope intercept y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values }\\ \qquad \uparrow\\ \textit{point-slope form}\)
hmm looks like he has it :~>jdoe can help.
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?

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Im gonna guess that its D because its the only one with x+2
-4/2 would be run/rise though :)
Than 2/-4 ;D So than it would be y-5=-2/4(x+2)?
yeap, just bear in mind that \(\bf -\cfrac{\cancel{2}}{\cancel{4}}\iff -\cfrac{1}{2}\)
So then whats next?
hmmm hold the mayo... ... lemme recheck that
ohhh you have a -5....hmm
I put that because of the y1
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 \(\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({\color{red}{ -2}}\quad ,&{\color{blue}{ -5}})\quad % (c,d) &({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}}) \end{array} \\\quad \\ % slope = m slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies -\cfrac{\cancel{8}}{\cancel{4}}\implies -2 \\ \quad \\ % point-slope intercept y-{\color{blue}{ 3}}={\color{green}{ -2}}(x-{\color{red}{ 2}})\qquad \textit{plug in the values }\\ \qquad \uparrow\\ \textit{point-slope form}\)
But thats not an answer choice xDDDDD
hmm
Wouldn't it be positive 2 as the rise/run because the negatives both cancel?
ohh yea... darn.. yes it's 3-(-5) = +8 and 2-(-2) = +4 yeap \(\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({\color{red}{ -2}}\quad ,&{\color{blue}{ -5}})\quad % (c,d) &({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}}) \end{array} \\\quad \\ % slope = m slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies \cfrac{\cancel{8}}{\cancel{4}}\implies 2 \\ \quad \\ % point-slope intercept y-{\color{blue}{ 3}}={\color{green}{ 2}}(x-{\color{red}{ 2}})\qquad \textit{plug in the values }\\ \qquad \uparrow\\ \textit{point-slope form}\)
Thanks for all your help!!

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