SOLUTION: Can someone please help me solve this problem. Write an equation of a line that passes through point (4,-9) and a slope of -4. Thank you

Algebra ->  Graphs -> SOLUTION: Can someone please help me solve this problem. Write an equation of a line that passes through point (4,-9) and a slope of -4. Thank you      Log On


   

Question 92390: Can someone please help me solve this problem.
Write an equation of a line that passes through point (4,-9) and a slope of -4.
Thank you
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 -4 which goes through the point (4,-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=%28-4%29%28x-4%29 Plug in m=-4, x%5B1%5D=4, and y%5B1%5D=-9 (these values are given)

y--9=%28-4%29x-%28-4%29%284%29%29 Distribute -4

y--9=%28-4%29x%2B%284%29%284%29%29 Multiply the negatives

y%2B9=%28-4%29x%2B16 Multiply 4 and 4 to get 16

y=%28-4%29x%2B16-9Subtract -9 from both sides


y=%28-4%29x%2B7 Combine like terms
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Answer:


So the equation of the line with a slope of -4 which goes through the point (4,-9) is:

y=-4x%2B7 which is now in y=mx%2Bb form where the slope is m=-4 and the y-intercept is b=7

Notice if we graph the equation y=-4x%2B7 and plot the point (4,-9), we get (note: if you need help with graphing, check out this solver)

Graph of y=-4x%2B7 through the point (4,-9)
and we can see that the point lies on the line. Since we know the equation has a slope of -4 and goes through the point (4,-9), this verifies our answer.