SOLUTION: Write the equation of the line that passes through point (0, –9) with a slope of 6

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Question 92287: Write the equation of the line that passes through point (0, –9) with a slope of 6
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 6 which goes through the point (0,-9), 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 (x%5B1%5D,y%5B1%5D) is the given point

So lets use the Point-Slope Formula to find the equation of the line

y--9=%286%29%28x-0%29 Plug in m=6, x%5B1%5D=0, and y%5B1%5D=-9 (these values are given)

y--9=%286%29x-%286%29%280%29%29 Distribute 6

y--9=%286%29x%2B%28-6%29%280%29%29 Multiply the negatives

y%2B9=%286%29x%2B0 Multiply -6 and 0 to get 0

y=%286%29x%2B0%2B-9Subtract -9 from both sides


y=6x-9 Combine like terms
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Answer:


So the equation of the line with a slope of 6 which goes through the point (0,-9) is:

y=6x-9 which is now in y=mx%2Bb form where the slope is m=6 and the y-intercept is b=-9

Notice if we graph the equation y=6x-9 and plot the point (0,-9), we get (note: if you need help with graphing, check out this solver)

Graph of y=6x-9 through the point (0,-9)
and we can see that the point lies on the line. Since we know the equation has a slope of 6 and goes through the point (0,-9), this verifies our answer.