SOLUTION: Find an equation of the line containing the point (-2,-5) and parallel to the line 4x-5y=13. I tried to solve the above problem and came up with the following answer: -5y/5=-4x/5

Algebra ->  Equations -> SOLUTION: Find an equation of the line containing the point (-2,-5) and parallel to the line 4x-5y=13. I tried to solve the above problem and came up with the following answer: -5y/5=-4x/5      Log On


   

Question 187172: Find an equation of the line containing the point (-2,-5) and parallel to the line 4x-5y=13.
I tried to solve the above problem and came up with the following answer:
-5y/5=-4x/5+13/5.... y=-4/5x+13/5 ...(slope=-4/5. The answer is supposed to be y=-4/5x+17/5. I don't understand where 17 came from.
Thank you for your help with this problem.
Judy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x-5y=13 Start with the given equation.


-5y=13-4x Subtract 4x from both sides.


-5y=-4x%2B13 Rearrange the terms.


y=%28-4x%2B13%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=%28%28-4%29%2F%28-5%29%29x%2B%2813%29%2F%28-5%29 Break up the fraction.


y=%284%2F5%29x-13%2F5 Reduce.


We can see that the equation y=%284%2F5%29x-13%2F5 has a slope m=4%2F5 and a y-intercept b=-13%2F5.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=4%2F5.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=4%2F5 and the coordinates of the given point .


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


y--5=%284%2F5%29%28x--2%29 Plug in m=4%2F5, x%5B1%5D=-2, and y%5B1%5D=-5


y--5=%284%2F5%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B5=%284%2F5%29%28x%2B2%29 Rewrite y--5 as y%2B5


y%2B5=%284%2F5%29x%2B%284%2F5%29%282%29 Distribute


y%2B5=%284%2F5%29x%2B8%2F5 Multiply


y=%284%2F5%29x%2B8%2F5-5 Subtract 5 from both sides.


y=%284%2F5%29x-17%2F5 Combine like terms.


So the equation of the line parallel to 4x-5y=13 that goes through the point is y=%284%2F5%29x-17%2F5.