SOLUTION: Write the equation of the line that passes through point (0, –2) with a slope of -7/2 .

Algebra ->  Coordinate-system -> SOLUTION: Write the equation of the line that passes through point (0, –2) with a slope of -7/2 .      Log On


   

Question 110802: Write the equation of the line that passes through point (0, –2) with a slope of -7/2 .
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 -7%2F2 which goes through the point (0,-2), 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--2=%28-7%2F2%29%28x-0%29 Plug in m=-7%2F2, x%5B1%5D=0, and y%5B1%5D=-2 (these values are given)


y%2B2=%28-7%2F2%29%28x-0%29 Rewrite y--2 as y%2B2


y%2B2=%28-7%2F2%29x%2B%28-7%2F2%29%28-0%29 Distribute -7%2F2

y%2B2=%28-7%2F2%29x%2B0 Multiply -7%2F2 and -0 to get 0

y=%28-7%2F2%29x%2B0-2 Subtract 2 from both sides to isolate y

y=%28-7%2F2%29x-2 Combine like terms 0 and -2 to get -2
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Answer:


So the equation of the line with a slope of -7%2F2 which goes through the point (0,-2) is:

y=%28-7%2F2%29x-2 which is now in y=mx%2Bb form where the slope is m=-7%2F2 and the y-intercept is b=-2

Notice if we graph the equation y=%28-7%2F2%29x-2 and plot the point (0,-2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-7%2F2%29x-2 through the point (0,-2)
and we can see that the point lies on the line. Since we know the equation has a slope of -7%2F2 and goes through the point (0,-2), this verifies our answer.