SOLUTION: A line passes through the point (x,y)=(-1,-4) and has a slope of 5. Write an equation for this line.

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Question 174343: A line passes through the point (x,y)=(-1,-4) and has a slope of 5. Write an equation for this line.
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 5 which goes through the point (-1,-4), 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--4=%285%29%28x--1%29 Plug in m=5, x%5B1%5D=-1, and y%5B1%5D=-4 (these values are given)


y%2B4=%285%29%28x--1%29 Rewrite y--4 as y%2B4


y%2B4=%285%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B4=5x%2B%285%29%281%29 Distribute 5

y%2B4=5x%2B5 Multiply 5 and 1 to get 5

y=5x%2B5-4 Subtract 4 from both sides to isolate y

y=5x%2B1 Combine like terms 5 and -4 to get 1
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Answer:


So the equation of the line with a slope of 5 which goes through the point (-1,-4) is:

y=5x%2B1 which is now in y=mx%2Bb form where the slope is m=5 and the y-intercept is b=1

Notice if we graph the equation y=5x%2B1 and plot the point (-1,-4), we get (note: if you need help with graphing, check out this solver)

Graph of y=5x%2B1 through the point (-1,-4)
and we can see that the point lies on the line. Since we know the equation has a slope of 5 and goes through the point (-1,-4), this verifies our answer.