SOLUTION: writ an equation of the line containing the given point and parallel to the givenline. express your answer in the form y=mx+b. (6,9), x+6y=7.... the equation of the line is y =

Algebra ->  Functions -> SOLUTION: writ an equation of the line containing the given point and parallel to the givenline. express your answer in the form y=mx+b. (6,9), x+6y=7.... the equation of the line is y =      Log On


   

Question 257320: writ an equation of the line containing the given point and parallel to the givenline. express your answer in the form y=mx+b. (6,9), x+6y=7.... the equation of the line is y =
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B6y=7 Start with the given equation.


6y=7-x Subtract x from both sides.


6y=-x%2B7 Rearrange the terms.


y=%28-x%2B7%29%2F%286%29 Divide both sides by 6 to isolate y.


y=%28%28-1%29%2F%286%29%29x%2B%287%29%2F%286%29 Break up the fraction.


y=-%281%2F6%29x%2B7%2F6 Reduce.


We can see that the equation y=-%281%2F6%29x%2B7%2F6 has a slope m=-1%2F6 and a y-intercept b=7%2F6.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-1%2F6.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-1%2F6 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=%28-1%2F6%29%28x-6%29 Plug in m=-1%2F6, x%5B1%5D=6, and y%5B1%5D=9


y-9=%28-1%2F6%29x%2B%28-1%2F6%29%28-6%29 Distribute


y-9=%28-1%2F6%29x%2B1 Multiply


y=%28-1%2F6%29x%2B1%2B9 Add 9 to both sides.


y=%28-1%2F6%29x%2B10 Combine like terms.


So the equation of the line parallel to x%2B6y=7 that goes through the point is y=%28-1%2F6%29x%2B10.


Here's a graph to visually verify our answer:

Graph of the original equation y=-%281%2F6%29x%2B7%2F6 (red) and the parallel line y=%28-1%2F6%29x%2B10 (green) through the point .