SOLUTION: Wrute an equation of line containing the given point and parallel to the given line. (9,-9)8x-9y=5 The equation of line is y=

Algebra ->  Linear-equations -> SOLUTION: Wrute an equation of line containing the given point and parallel to the given line. (9,-9)8x-9y=5 The equation of line is y=      Log On


   

Question 376310: Wrute an equation of line containing the given point and parallel to the given line.
(9,-9)8x-9y=5
The equation of line is y=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x-9y=5 Start with the given equation.


-9y=5-8x Subtract 8x from both sides.


-9y=-8x%2B5 Rearrange the terms.


y=%28-8x%2B5%29%2F%28-9%29 Divide both sides by -9 to isolate y.


y=%28%28-8%29%2F%28-9%29%29x%2B%285%29%2F%28-9%29 Break up the fraction.


y=%288%2F9%29x-5%2F9 Reduce.


We can see that the equation y=%288%2F9%29x-5%2F9 has a slope m=8%2F9 and a y-intercept b=-5%2F9.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=8%2F9.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=8%2F9 and the coordinates of the given point .


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


y--9=%288%2F9%29%28x-9%29 Plug in m=8%2F9, x%5B1%5D=9, and y%5B1%5D=-9


y%2B9=%288%2F9%29%28x-9%29 Rewrite y--9 as y%2B9


y%2B9=%288%2F9%29x%2B%288%2F9%29%28-9%29 Distribute


y%2B9=%288%2F9%29x-8 Multiply


y=%288%2F9%29x-8-9 Subtract 9 from both sides.


y=%288%2F9%29x-17 Combine like terms.


So the equation of the line parallel to 8x-9y=5 that goes through the point is y=%288%2F9%29x-17.


Here's a graph to visually verify our answer:
Graph of the original equation y=%288%2F9%29x-5%2F9 (red) and the parallel line y=%288%2F9%29x-17 (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim