SOLUTION: Hello. Can I have help finding the equation of the line parallel to y=2x+3 passing through (1,1) thanks Haley

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Question 180581: Hello.
Can I have help finding the equation of the line parallel to y=2x+3 passing through (1,1)
thanks
Haley
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


We can see that the equation y=2%2Ax%2B3 has a slope m=2 and a y-intercept b=3.


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


y-1=2x%2B2%28-1%29 Distribute


y-1=2x-2 Multiply


y=2x-2%2B1 Add 1 to both sides.


y=2x-1 Combine like terms.


So the equation of the line parallel to -2x%2By=3 that goes through the point is y=2x-1.


Here's a graph to visually verify our answer:
Graph of the original equation y=2%2Ax%2B3 (red) and the parallel line y=2x-1 (green) through the point .