anonymous
  • anonymous
passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?
Mathematics
chestercat
  • chestercat
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Michele_Laino
  • Michele_Laino
hint: equation for the line which passes at point A and at point B, is: \[\Large \frac{{x - x1}}{{{x_2} - {x_1}}} = \frac{{y - {y_1}}}{{{y_2} - {y_1}}}\] where A=(x1,y1) and B=(x2,y2) Now you have to substitute the coordinates of both points A and B, in order to to write the corresponding equation
anonymous
  • anonymous
i have no idea im clueless
Michele_Laino
  • Michele_Laino
your exercise asks for the equation of the line parallel to the line which passes at points A and B, right?

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anonymous
  • anonymous
yes
Michele_Laino
  • Michele_Laino
so, we have to write the equation which passes at point A and B, first
anonymous
  • anonymous
ok
Michele_Laino
  • Michele_Laino
in order to do that, you have to substitute the coordinates of your points A and B into the equation above
anonymous
  • anonymous
ok
Michele_Laino
  • Michele_Laino
please try!
anonymous
  • anonymous
haha im trying but i dont understand the equation
anonymous
  • anonymous
ive never seen it like that
anonymous
  • anonymous
the question asks line ab passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to line ab ?
Michele_Laino
  • Michele_Laino
ok! Here is the procedure: we have this: \[\Large \begin{gathered} {x_1} = - 3,\quad {x_2} = - 6 \hfill \\ {y_1} = 0,\quad {y_2} = 5 \hfill \\ \end{gathered} \]
anonymous
  • anonymous
ok
anonymous
  • anonymous
i need like help fast class ends in 5 mins and i have 1 more question after so i wrote the equation from your thing now what?
Michele_Laino
  • Michele_Laino
now, I substitute those value into my equation above, and I get: \[\Large \frac{{x - \left( { - 3} \right)}}{{ - 6 - \left( { - 3} \right)}} = \frac{{y - 0}}{{5 - 0}}\]
anonymous
  • anonymous
yes i got that
Michele_Laino
  • Michele_Laino
now I can simplify as below: \[\Large \begin{gathered} \frac{y}{5} = \frac{{x + 3}}{{ - 6 + 3}} \hfill \\ \hfill \\ \frac{y}{5} = \frac{{x + 3}}{{ - 3}} \hfill \\ \hfill \\ y = - \frac{5}{3}\left( {x + 3} \right) \hfill \\ \end{gathered} \]
anonymous
  • anonymous
parallel to that is?
Michele_Laino
  • Michele_Laino
no, the requested line, being parallel to that line has to have the same slope, in other words the slope of the requested parallel line is: \[\Large m = - \frac{5}{3}\]
Michele_Laino
  • Michele_Laino
since parallel lines have the same slope
Michele_Laino
  • Michele_Laino
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Michele_Laino
  • Michele_Laino
both lines have the same slope m= -5/3

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