SOLUTION: I am really having difficulty solving this problem: Write the equation of the line with slope –2 and y-intercept (0, 0). Then graph the line. Thanks for you help!

Algebra ->  Graphs -> SOLUTION: I am really having difficulty solving this problem: Write the equation of the line with slope –2 and y-intercept (0, 0). Then graph the line. Thanks for you help!      Log On


   

Question 93643: I am really having difficulty solving this problem:
Write the equation of the line with slope –2 and y-intercept (0, 0). Then graph the line.
Thanks for you help!
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 (0,0), 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-0=%28-2%29%28x-0%29 Plug in m=-2, x%5B1%5D=0, and y%5B1%5D=0 (these values are given)


y-0=-2x%2B%28-2%29%28-0%29 Distribute -2

y-0=-2x%2B0 Multiply -2 and -0 to get 0

y=-2x%2B0%2B0 Add 0 to both sides to isolate y

y=-2x%2B0 Combine like terms

y=-2x Remove any zero terms
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Answer:


So the equation of the line with a slope of -2 which goes through the point (0,0) is:

y=-2x which is now in y=mx%2Bb form where the slope is m=-2 and the y-intercept is b=0

Notice if we graph the equation y=-2x and plot the point (0,0), we get (note: if you need help with graphing, check out this solver)

Graph of y=-2x through the point (0,0)
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 (0,0), this verifies our answer.