Find k so that the line containing the points (-5,k) and (2,10) is parallel to the line containing the points (5,5) and (1,-4)

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asked Feb 22, 2018 102k views

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Slothworks · Answer 1 · 2018-02-26T14:33:50+0000

if the line containing the coordinate "k", is parallel to the line at 5,5 and 1,-4, then their slopes must be the same, since parallel lines, have the same slope, let's check both slopes then.

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 5}}\quad ,&{{ 5}})\quad % (c,d) &({{ 1}}\quad ,&{{ -4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-5}{1-5}\implies \cfrac{-9}{-4}\implies \boxed{\cfrac{9}{4}}\\\\ -------------------------------\\\\$

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -5}}\quad ,&{{ k}})\quad % (c,d) &({{ 2}}\quad ,&{{ 10}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-k}{2-(-5)}\implies \cfrac{10-k}{2+5} \\\\\\ \stackrel{\textit{parallel lines, same slope}}{\cfrac{10-k}{7}=\boxed{\cfrac{9}{4}}}\implies 40-4k=63\implies -23=4k\implies -\cfrac{23}{4}=k$

Find k so that the line containing the points (-5,k) and (2,10) is parallel to the line containing the points (5,5) and (1,-4)

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