SOLUTION: Write an equation of the line containing the given point and parallel to the given line. (4,-4), 2x-7y=3 The equation of the line is y=? Simplify the answer. Can anyone help me

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line containing the given point and parallel to the given line. (4,-4), 2x-7y=3 The equation of the line is y=? Simplify the answer. Can anyone help me      Log On


   

Question 243547: Write an equation of the line containing the given point and parallel to the given line.
(4,-4), 2x-7y=3
The equation of the line is y=?
Simplify the answer.
Can anyone help me on this one it really has me stumped. Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-7y=3 Start with the given equation.


-7y=3-2x Subtract 2x from both sides.


-7y=-2x%2B3 Rearrange the terms.


y=%28-2x%2B3%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=%28%28-2%29%2F%28-7%29%29x%2B%283%29%2F%28-7%29 Break up the fraction.


y=%282%2F7%29x-3%2F7 Reduce.


We can see that the equation y=%282%2F7%29x-3%2F7 has a slope m=2%2F7 and a y-intercept b=-3%2F7.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=2%2F7.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=2%2F7 and the coordinates of the given point .


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


y--4=%282%2F7%29%28x-4%29 Plug in m=2%2F7, x%5B1%5D=4, and y%5B1%5D=-4


y%2B4=%282%2F7%29%28x-4%29 Rewrite y--4 as y%2B4


y%2B4=%282%2F7%29x%2B%282%2F7%29%28-4%29 Distribute


y%2B4=%282%2F7%29x-8%2F7 Multiply


y=%282%2F7%29x-8%2F7-4 Subtract 4 from both sides.


y=%282%2F7%29x-36%2F7 Combine like terms.


So the equation of the line parallel to 2x-7y=3 that goes through the point is y=%282%2F7%29x-36%2F7.


Here's a graph to visually verify our answer:

Graph of the original equation y=%282%2F7%29x-3%2F7 (red) and the parallel line y=%282%2F7%29x-36%2F7 (green) through the point .