SOLUTION: find a linear function whose graph has a slope = -3 and a y intercept of (0, -5)

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Question 127321: find a linear function whose graph has a slope = -3 and a y intercept of (0, -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 -3 which goes through the point (0,-5), 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--5=%28-3%29%28x-0%29 Plug in m=-3, x%5B1%5D=0, and y%5B1%5D=-5 (these values are given)


y%2B5=%28-3%29%28x-0%29 Rewrite y--5 as y%2B5


y%2B5=-3x%2B%28-3%29%28-0%29 Distribute -3

y%2B5=-3x%2B0 Multiply -3 and -0 to get 0

y=-3x%2B0-5 Subtract 5 from both sides to isolate y

y=-3x-5 Combine like terms 0 and -5 to get -5
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Answer:


So the equation of the line with a slope of -3 which goes through the point (0,-5) is:

y=-3x-5 which is now in y=mx%2Bb form where the slope is m=-3 and the y-intercept is b=-5

Notice if we graph the equation y=-3x-5 and plot the point (0,-5), we get (note: if you need help with graphing, check out this solver)

Graph of y=-3x-5 through the point (0,-5)
and we can see that the point lies on the line. Since we know the equation has a slope of -3 and goes through the point (0,-5), this verifies our answer.