SOLUTION: The line through (-2,-1) that is parallel to the line 5x + 3y =9. I am having a horrible time trying to write solve this and then write it into standard form containing only integ

Algebra ->  Graphs -> SOLUTION: The line through (-2,-1) that is parallel to the line 5x + 3y =9. I am having a horrible time trying to write solve this and then write it into standard form containing only integ      Log On


   

Question 181882: The line through (-2,-1) that is parallel to the line 5x + 3y =9. I am having a horrible time trying to write solve this and then write it into standard form containing only integer coefficients.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5x+%2B+3y+=9 Start with the given equation.


3y=-5x%2B9 Rearrange the terms.


y=%28-5x%2B9%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%28-5%29%2F%283%29%29x%2B%289%29%2F%283%29 Break up the fraction.


y=-%285%2F3%29x%2B3 Reduce.


We can see that the equation y=-%285%2F3%29x%2B3 has a slope m=-5%2F3 and a y-intercept b=3.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-5%2F3.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-5%2F3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--1=%28-5%2F3%29%28x--2%29 Plug in m=-5%2F3, x%5B1%5D=-2, and y%5B1%5D=-1


y--1=%28-5%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B1=%28-5%2F3%29%28x%2B2%29 Rewrite y--1 as y%2B1


3%28y%2B1%29=-5%28x%2B2%29 Multiply both sides by 3.


3y%2B3=-5x-10 Distribute


3y%2B3%2B5x=-10 Add 5x to both sides.


3y%2B5x=-10-3 Subtract 3 from both sides.


5x%2B3y=-13 Combine and rearrange the terms.



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Answer:

So the equation of the line that is parallel to 5x+%2B+3y+=9 and that goes through (-2,-1) is: 5x%2B3y=-13


Also, the equation is in standard form Ax%2BBy=C where A=5, B=3, and C=-13