SOLUTION: (-6,5);8x=5y+2 Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b

Algebra ->  Graphs -> SOLUTION: (-6,5);8x=5y+2 Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b      Log On


   

Question 154327: (-6,5);8x=5y+2
Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8x=5y%2B2 Start with the given equation.


8x-2=5y Subtract 2 from both sides.


%288x-2%29%2F5=y Divide both sides by 5.



%288x%29%2F5-%282%29%2F5=y Break up the fraction


%288%2F5%29x-2%2F5=y Simplify


So after converting 8x=5y%2B2 into slope-intercept form, we get y=%288%2F5%29x-2%2F5


We can see that the equation y=%288%2F5%29x-2%2F5 has a slope m=8%2F5 and a y-intercept b=-2%2F5.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=8%2F5.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=8%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=%288%2F5%29%28x--6%29 Plug in m=8%2F5, x%5B1%5D=-6, and y%5B1%5D=5


y-5=%288%2F5%29%28x%2B6%29 Rewrite x--6 as x%2B6


y-5=%288%2F5%29x%2B%288%2F5%29%286%29 Distribute


y-5=%288%2F5%29x%2B48%2F5 Multiply


y=%288%2F5%29x%2B48%2F5%2B5 Add 5 to both sides.


y=%288%2F5%29x%2B73%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to 8x=5y%2B2 that goes through the point is y=%288%2F5%29x%2B73%2F5.


Here's a graph to visually verify our answer:
Graph of the original equation y=%288%2F5%29x-2%2F5 (red) and the parallel line y=%288%2F5%29x%2B73%2F5 (green) through the point .