SOLUTION: Hello! Write an equation of the line containing the given point and parallel to the given line. Express your answer in y = mx+b. (5,9;) 9x+y = 7

Algebra ->  Linear-equations -> SOLUTION: Hello! Write an equation of the line containing the given point and parallel to the given line. Express your answer in y = mx+b. (5,9;) 9x+y = 7      Log On


   

Question 375911: Hello!
Write an equation of the line containing the given point and parallel to the given line. Express your answer in y = mx+b.
(5,9;) 9x+y = 7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%2By=7 Start with the given equation.


y=7-9x Subtract 9x from both sides.


y=-9x%2B7 Rearrange the terms.


We can see that the equation y=-9%2Ax%2B7 has a slope m=-9 and a y-intercept b=7.


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


y-9=-9x%2B-9%28-5%29 Distribute


y-9=-9x%2B45 Multiply


y=-9x%2B45%2B9 Add 9 to both sides.


y=-9x%2B54 Combine like terms.


So the equation of the line parallel to 9x%2By=7 that goes through the point is y=-9x%2B54.


Here's a graph to visually verify our answer:
Graph of the original equation y=-9%2Ax%2B7 (red) and the parallel line y=-9x%2B54 (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