Find the equation of a line with gradient -2/3 through the point (4,-6). Give your answer in the form ax+by+c=0 where a is a positive integer. [on hold]

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I am given the formula $$ax+by+c=0$$ the point $(4,-6)$ and the slope $-2/3$. I am asked to find $a$,$b$, and $c$. I have been trying to find results for a while. It says $a$ is a positive integer but that doesn't make sense to me since $m=- 2/3$.



I have never encountered a question like this and I have no idea how to tackle it...




geometry




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put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.












  • hint: $m=-fracab$
    – Vasya
    Aug 28 at 12:58











  • You can always multiply both sides by $-1$ at the end to make $a$ positive.
    – amd
    Aug 28 at 19:36










  • Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
    – Narasimham
    Sep 7 at 19:48















up vote
0
down vote

favorite












I am given the formula $$ax+by+c=0$$ the point $(4,-6)$ and the slope $-2/3$. I am asked to find $a$,$b$, and $c$. I have been trying to find results for a while. It says $a$ is a positive integer but that doesn't make sense to me since $m=- 2/3$.



I have never encountered a question like this and I have no idea how to tackle it...




geometry




share|cite|improve this question














put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.












  • hint: $m=-fracab$
    – Vasya
    Aug 28 at 12:58











  • You can always multiply both sides by $-1$ at the end to make $a$ positive.
    – amd
    Aug 28 at 19:36










  • Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
    – Narasimham
    Sep 7 at 19:48













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I am given the formula $$ax+by+c=0$$ the point $(4,-6)$ and the slope $-2/3$. I am asked to find $a$,$b$, and $c$. I have been trying to find results for a while. It says $a$ is a positive integer but that doesn't make sense to me since $m=- 2/3$.



I have never encountered a question like this and I have no idea how to tackle it...




geometry




share|cite|improve this question














I am given the formula $$ax+by+c=0$$ the point $(4,-6)$ and the slope $-2/3$. I am asked to find $a$,$b$, and $c$. I have been trying to find results for a while. It says $a$ is a positive integer but that doesn't make sense to me since $m=- 2/3$.



I have never encountered a question like this and I have no idea how to tackle it...





geometry





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share|cite|improve this question




share|cite|improve this question








edited Aug 28 at 14:06









Chris Godsil

11.1k21534




11.1k21534










asked Aug 28 at 12:56









Mihai Munteanu

62




62




put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Jyrki Lahtonen, John Ma, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.











  • hint: $m=-fracab$
    – Vasya
    Aug 28 at 12:58











  • You can always multiply both sides by $-1$ at the end to make $a$ positive.
    – amd
    Aug 28 at 19:36










  • Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
    – Narasimham
    Sep 7 at 19:48

















  • hint: $m=-fracab$
    – Vasya
    Aug 28 at 12:58











  • You can always multiply both sides by $-1$ at the end to make $a$ positive.
    – amd
    Aug 28 at 19:36










  • Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
    – Narasimham
    Sep 7 at 19:48
















hint: $m=-fracab$
– Vasya
Aug 28 at 12:58





hint: $m=-fracab$
– Vasya
Aug 28 at 12:58













You can always multiply both sides by $-1$ at the end to make $a$ positive.
– amd
Aug 28 at 19:36




You can always multiply both sides by $-1$ at the end to make $a$ positive.
– amd
Aug 28 at 19:36












Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
– Narasimham
Sep 7 at 19:48





Can you bring it to $ y=mx+c,,$( slope ,- $y,$ intercept) form?
– Narasimham
Sep 7 at 19:48











2 Answers
2






active

oldest

votes

















up vote
0
down vote



accepted










The searched equation has the form $$y=-frac23x+n$$ since we have given $$x=4,y=-6$$ we get for $n$:
$$n=-6+frac83=-frac103$$



Can you proceed?



The result should be $$2x+3y+10=0$$






share|cite|improve this answer




















  • sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
    – Mihai Munteanu
    Aug 28 at 13:26

















up vote
0
down vote













Hint: General Equation of a line with slope $m$ and passing through a point $(x_1,y_1)$ is:



$y-y_1=m(x-x_1)$.



Put the values in the above equation and then rearrange in the form $ax+by+c=0$.



So with the above values, the equation becomes :



$y-(-6)=-frac23(x-4)$



$ implies 3(y+6)=-2(x-4)$



$ implies3y+18=-2x+8$



$implies 3y+2x+10=0$






share|cite|improve this answer






















  • @MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
    – paulplusx
    Aug 28 at 13:56

















2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote



accepted










The searched equation has the form $$y=-frac23x+n$$ since we have given $$x=4,y=-6$$ we get for $n$:
$$n=-6+frac83=-frac103$$



Can you proceed?



The result should be $$2x+3y+10=0$$






share|cite|improve this answer




















  • sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
    – Mihai Munteanu
    Aug 28 at 13:26














up vote
0
down vote



accepted










The searched equation has the form $$y=-frac23x+n$$ since we have given $$x=4,y=-6$$ we get for $n$:
$$n=-6+frac83=-frac103$$



Can you proceed?



The result should be $$2x+3y+10=0$$






share|cite|improve this answer




















  • sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
    – Mihai Munteanu
    Aug 28 at 13:26












up vote
0
down vote



accepted







up vote
0
down vote



accepted






The searched equation has the form $$y=-frac23x+n$$ since we have given $$x=4,y=-6$$ we get for $n$:
$$n=-6+frac83=-frac103$$



Can you proceed?



The result should be $$2x+3y+10=0$$






share|cite|improve this answer












The searched equation has the form $$y=-frac23x+n$$ since we have given $$x=4,y=-6$$ we get for $n$:
$$n=-6+frac83=-frac103$$



Can you proceed?



The result should be $$2x+3y+10=0$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 28 at 13:01









Dr. Sonnhard Graubner

68.2k32760




68.2k32760











  • sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
    – Mihai Munteanu
    Aug 28 at 13:26
















  • sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
    – Mihai Munteanu
    Aug 28 at 13:26















sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
– Mihai Munteanu
Aug 28 at 13:26




sorry but I don't really get where you got the 2,3 and 10 from can you maybe add a few more steps, explain it like I am 5?
– Mihai Munteanu
Aug 28 at 13:26










up vote
0
down vote













Hint: General Equation of a line with slope $m$ and passing through a point $(x_1,y_1)$ is:



$y-y_1=m(x-x_1)$.



Put the values in the above equation and then rearrange in the form $ax+by+c=0$.



So with the above values, the equation becomes :



$y-(-6)=-frac23(x-4)$



$ implies 3(y+6)=-2(x-4)$



$ implies3y+18=-2x+8$



$implies 3y+2x+10=0$






share|cite|improve this answer






















  • @MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
    – paulplusx
    Aug 28 at 13:56














up vote
0
down vote













Hint: General Equation of a line with slope $m$ and passing through a point $(x_1,y_1)$ is:



$y-y_1=m(x-x_1)$.



Put the values in the above equation and then rearrange in the form $ax+by+c=0$.



So with the above values, the equation becomes :



$y-(-6)=-frac23(x-4)$



$ implies 3(y+6)=-2(x-4)$



$ implies3y+18=-2x+8$



$implies 3y+2x+10=0$






share|cite|improve this answer






















  • @MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
    – paulplusx
    Aug 28 at 13:56












up vote
0
down vote










up vote
0
down vote









Hint: General Equation of a line with slope $m$ and passing through a point $(x_1,y_1)$ is:



$y-y_1=m(x-x_1)$.



Put the values in the above equation and then rearrange in the form $ax+by+c=0$.



So with the above values, the equation becomes :



$y-(-6)=-frac23(x-4)$



$ implies 3(y+6)=-2(x-4)$



$ implies3y+18=-2x+8$



$implies 3y+2x+10=0$






share|cite|improve this answer














Hint: General Equation of a line with slope $m$ and passing through a point $(x_1,y_1)$ is:



$y-y_1=m(x-x_1)$.



Put the values in the above equation and then rearrange in the form $ax+by+c=0$.



So with the above values, the equation becomes :



$y-(-6)=-frac23(x-4)$



$ implies 3(y+6)=-2(x-4)$



$ implies3y+18=-2x+8$



$implies 3y+2x+10=0$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 28 at 13:58

























answered Aug 28 at 13:03









paulplusx

686116




686116











  • @MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
    – paulplusx
    Aug 28 at 13:56
















  • @MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
    – paulplusx
    Aug 28 at 13:56















@MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
– paulplusx
Aug 28 at 13:56




@MihaiMunteanu If you cannot understand this then you should brush up your equation solving skills as well as Geometry (at least for Lines)
– paulplusx
Aug 28 at 13:56


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