## anonymous one year ago 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 ?

1. 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

2. anonymous

i have no idea im clueless

3. Michele_Laino

your exercise asks for the equation of the line parallel to the line which passes at points A and B, right?

4. anonymous

yes

5. Michele_Laino

so, we have to write the equation which passes at point A and B, first

6. anonymous

ok

7. Michele_Laino

in order to do that, you have to substitute the coordinates of your points A and B into the equation above

8. anonymous

ok

9. Michele_Laino

10. anonymous

haha im trying but i dont understand the equation

11. anonymous

ive never seen it like that

12. 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 ?

13. Michele_Laino

ok! Here is the procedure: we have this: $\Large \begin{gathered} {x_1} = - 3,\quad {x_2} = - 6 \hfill \\ {y_1} = 0,\quad {y_2} = 5 \hfill \\ \end{gathered}$

14. anonymous

ok

15. 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?

16. Michele_Laino

now, I substitute those value into my equation above, and I get: $\Large \frac{{x - \left( { - 3} \right)}}{{ - 6 - \left( { - 3} \right)}} = \frac{{y - 0}}{{5 - 0}}$

17. anonymous

yes i got that

18. Michele_Laino

now I can simplify as below: $\Large \begin{gathered} \frac{y}{5} = \frac{{x + 3}}{{ - 6 + 3}} \hfill \\ \hfill \\ \frac{y}{5} = \frac{{x + 3}}{{ - 3}} \hfill \\ \hfill \\ y = - \frac{5}{3}\left( {x + 3} \right) \hfill \\ \end{gathered}$

19. anonymous

parallel to that is?

20. 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: $\Large m = - \frac{5}{3}$

21. Michele_Laino

since parallel lines have the same slope

22. Michele_Laino

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23. Michele_Laino

both lines have the same slope m= -5/3