SOLUTION: If you dont't mind could you please help me solve this problem: Find the equation of the line that has slope 2 and passes throught (1,-3). Please show your work. Thank you, I mo

Algebra ->  Linear-equations -> SOLUTION: If you dont't mind could you please help me solve this problem: Find the equation of the line that has slope 2 and passes throught (1,-3). Please show your work. Thank you, I mo      Log On


   

Question 99376: If you dont't mind could you please help me solve this problem: Find the equation of the line that has slope 2 and passes throught (1,-3). Please show your work.
Thank you, I most appreciate it
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,-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=%282%29%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=-3 (these values are given)


y%2B3=%282%29%28x-1%29 Rewrite y--3 as y%2B3


y%2B3=2x%2B%282%29%28-1%29 Distribute 2

y%2B3=2x-2 Multiply 2 and -1 to get -2

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

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


So the equation of the line with a slope of 2 which goes through the point (1,-3) is:

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

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

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