SOLUTION: Find the equation of a line through the point (2,-1) with a slope 4

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Question 199536: Find the equation of a line through the point
(2,-1) with a slope 4
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 4 which goes through the point (2,-1), 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--1=%284%29%28x-2%29 Plug in m=4, x%5B1%5D=2, and y%5B1%5D=-1 (these values are given)


y%2B1=%284%29%28x-2%29 Rewrite y--1 as y%2B1


y%2B1=4x%2B%284%29%28-2%29 Distribute 4

y%2B1=4x-8 Multiply 4 and -2 to get -8

y=4x-8-1 Subtract 1 from both sides to isolate y

y=4x-9 Combine like terms -8 and -1 to get -9
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Answer:


So the equation of the line with a slope of 4 which goes through the point (2,-1) is:

y=4x-9 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=-9

Notice if we graph the equation y=4x-9 and plot the point (2,-1), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x-9 through the point (2,-1)
and we can see that the point lies on the line. Since we know the equation has a slope of 4 and goes through the point (2,-1), this verifies our answer.