SOLUTION: Question: Write an equation of the line that passes through each point with the given slope. (-1,-3),m=5

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Question 175490: Question: Write an equation of the line that passes through each point with the given slope. (-1,-3),m=5
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,-3), 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--3=%285%29%28x--1%29 Plug in m=5, x%5B1%5D=-1, and y%5B1%5D=-3 (these values are given)


y%2B3=%285%29%28x--1%29 Rewrite y--3 as y%2B3


y%2B3=%285%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B3=5x%2B%285%29%281%29 Distribute 5

y%2B3=5x%2B5 Multiply 5 and 1 to get 5

y=5x%2B5-3 Subtract 3 from both sides to isolate y

y=5x%2B2 Combine like terms 5 and -3 to get 2
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Answer:


So the equation of the line with a slope of 5 which goes through the point (-1,-3) is:

y=5x%2B2 which is now in y=mx%2Bb form where the slope is m=5 and the y-intercept is b=2

Notice if we graph the equation y=5x%2B2 and plot the point (-1,-3), we get (note: if you need help with graphing, check out this solver)

Graph of y=5x%2B2 through the point (-1,-3)
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,-3), this verifies our answer.