SOLUTION: Find an equation of the line that is parallel to the line y=4x+5 and that passes through the point (-3,-2).

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Question 336496: Find an equation of the line that is parallel to the line y=4x+5 and that passes through the point (-3,-2).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=4x%2B5 has a slope m=4 and a y-intercept b=5.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=4.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=4 and the coordinates of the given point .


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


y--2=4%28x--3%29 Plug in m=4, x%5B1%5D=-3, and y%5B1%5D=-2


y--2=4%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B2=4%28x%2B3%29 Rewrite y--2 as y%2B2


y%2B2=4x%2B4%283%29 Distribute


y%2B2=4x%2B12 Multiply


y=4x%2B12-2 Subtract 2 from both sides.


y=4x%2B10 Combine like terms.


So the equation of the line parallel to y=4x%2B5 that goes through the point is y=4x%2B10.


Here's a graph to visually verify our answer:
Graph of the original equation y=4x%2B5 (red) and the parallel line y=4x%2B10 (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim