SOLUTION: Slope -2/5; y-intercept (0,4)

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Question 115430: Slope -2/5; y-intercept (0,4)
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%2F5 which goes through the point (0,4), 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=%28-2%2F5%29%28x-0%29 Plug in m=-2%2F5, x%5B1%5D=0, and y%5B1%5D=4 (these values are given)


y-4=%28-2%2F5%29x%2B%28-2%2F5%29%28-0%29 Distribute -2%2F5

y-4=%28-2%2F5%29x%2B0 Multiply -2%2F5 and -0 to get 0

y=%28-2%2F5%29x%2B0%2B4 Add 4 to both sides to isolate y

y=%28-2%2F5%29x%2B4 Combine like terms 0 and 4 to get 4
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Answer:


So the equation of the line with a slope of -2%2F5 which goes through the point (0,4) is:

y=%28-2%2F5%29x%2B4 which is now in y=mx%2Bb form where the slope is m=-2%2F5 and the y-intercept is b=4

Notice if we graph the equation y=%28-2%2F5%29x%2B4 and plot the point (0,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F5%29x%2B4 through the point (0,4)
and we can see that the point lies on the line. Since we know the equation has a slope of -2%2F5 and goes through the point (0,4), this verifies our answer.