SOLUTION: write an equation of the line containg the given point and parrel to the given line express your answer in the form of y=mx+b (4,8); x+4y=7

Algebra ->  Linear-equations -> SOLUTION: write an equation of the line containg the given point and parrel to the given line express your answer in the form of y=mx+b (4,8); x+4y=7      Log On


   

Question 174262: write an equation of the line containg the given point and parrel to the given line express your answer in the form of y=mx+b
(4,8); x+4y=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B4y=7 Start with the given equation.


4y=7-x Subtract x from both sides.


4y=-x%2B7 Rearrange the terms.


y=%28-x%2B7%29%2F%284%29 Divide both sides by 4 to isolate y.


y=%28%28-1%29%2F%284%29%29x%2B%287%29%2F%284%29 Break up the fraction.


y=-%281%2F4%29x%2B7%2F4 Reduce.


We can see that the equation y=-%281%2F4%29x%2B7%2F4 has a slope m=-1%2F4 and a y-intercept b=7%2F4.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-1%2F4.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-1%2F4 and the coordinates of the given point .


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


y-8=%28-1%2F4%29%28x-4%29 Plug in m=-1%2F4, x%5B1%5D=4, and y%5B1%5D=8


y-8=%28-1%2F4%29x%2B%28-1%2F4%29%28-4%29 Distribute


y-8=%28-1%2F4%29x%2B1 Multiply


y=%28-1%2F4%29x%2B1%2B8 Add 8 to both sides.


y=%28-1%2F4%29x%2B9 Combine like terms.


So the equation of the line parallel to x%2B4y=7 that goes through the point is y=%28-1%2F4%29x%2B9.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%281%2F4%29x%2B7%2F4 (red) and the parallel line y=%28-1%2F4%29x%2B9 (green) through the point .