SOLUTION: Hi! Can I have some help on finding an equation of the line through (1, 5) with slope 2?

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Question 124397: Hi!
Can I have some help on finding an equation of the line through (1, 5) with slope 2?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of 2 which goes through the point (1,5), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-5=%282%29%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=5 (these values are given)


y-5=2x%2B%282%29%28-1%29 Distribute 2

y-5=2x-2 Multiply 2 and -1 to get -2

y=2x-2%2B5 Add 5 to both sides to isolate y

y=2x%2B3 Combine like terms -2 and 5 to get 3
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Answer:


So the equation of the line with a slope of 2 which goes through the point (1,5) is:

y=2x%2B3 which is now in y=mx%2Bb form where the slope is m=2 and the y-intercept is b=3

Notice if we graph the equation y=2x%2B3 and plot the point (1,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=2x%2B3 through the point (1,5)
and we can see that the point lies on the line. Since we know the equation has a slope of 2 and goes through the point (1,5), this verifies our answer.