102k views
1 vote
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)

User BobG
by
7.6k points

1 Answer

6 votes
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
User Slothworks
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories