SOLUTION: Give the equation of the line that passes through point (-5, -1) and is parallel to the line y= -1/4x-7. Please help I am trying to work this problem and I do not remember how t

Algebra ->  Equations -> SOLUTION: Give the equation of the line that passes through point (-5, -1) and is parallel to the line y= -1/4x-7. Please help I am trying to work this problem and I do not remember how t      Log On


   

Question 309695: Give the equation of the line that passes through point (-5, -1) and is parallel to the line y= -1/4x-7.
Please help I am trying to work this problem and I do not remember how to work it.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-%281%2F4%29x-7 has a slope m=-1%2F4 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=-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--1=%28-1%2F4%29%28x--5%29 Plug in m=-1%2F4, x%5B1%5D=-5, and y%5B1%5D=-1


y--1=%28-1%2F4%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B1=%28-1%2F4%29%28x%2B5%29 Rewrite y--1 as y%2B1


y%2B1=%28-1%2F4%29x%2B%28-1%2F4%29%285%29 Distribute


y%2B1=%28-1%2F4%29x-5%2F4 Multiply


y=%28-1%2F4%29x-5%2F4-1 Subtract 1 from both sides.


y=%28-1%2F4%29x-9%2F4 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to y=-1%2F4x-7 that goes through the point is y=%28-1%2F4%29x-9%2F4.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%281%2F4%29x-7 (red) and the parallel line y=%28-1%2F4%29x-9%2F4 (green) through the point .