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Answer:
y = -17/6x -7/3
Step-by-step explanation:
The 2-point form of the equation for a line can be a useful place to start.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (-8 -9)/(2-(-4))(x -(-4)) +9
y = -17/6(x +4) +9 . . . . . simplify a bit
y = -17/6x -11 1/3 +9 . . . eliminate parentheses
y = -17/6x -7/3 . . . . . . . collect terms
Let x be the amount of neutral solution we need to add.
Since we have 40 fl of 5% local anesthesia solution, we have
fl of pure anesthesia.
After adding neutral solution, our new volume will be
. Remember that the concentration of the anesthesia after adding neutral solution should be 5%=0.05, and since the volume of the pure anesthesia won't change, we can relate all the values with the equation:
We can conclude that we will need to add 10 fl of neutral solution to our 40 fl of 5% anesthesia solution to get 50 fl of 4% anesthesia solution.
Since we have 40 fl of 5% local anesthesia solution, we have
After adding neutral solution, our new volume will be
We can conclude that we will need to add 10 fl of neutral solution to our 40 fl of 5% anesthesia solution to get 50 fl of 4% anesthesia solution.