The equation of the straight line is y=mx+q where q is the number on the y-axis where the line passes, as you can see it is -3. It turns into:
y=mx+(-3) -> y=mx-3
Then consider a point on the line and take the coordinates, such as the point with coordinates (-2;-4), so now you know that:
x=-2 and y=-4
At this point you put these values into the equation:
y=mx-3
-4=m(-2)-3
then solve:
-4=-2m-3
-2m=+3-4
-2m=-1
m=+1/2
Put the value of m into the equation and you found it:
y=1/2x-3
There would probably be multiple ways to solve this, but I will only show you one of them.
First, we need to figure out how many tablespoons of the chemical solution it takes to decrease the number of bacteria in a gallon to 300. So we subtract 1200 by 300, to find the number of unnecessary bacteria, which is 900. Now we divide 900 by 75, which is 12. So it would take 12 tablespoons of the chemical solution to make a gallon have 300 bacteria.
There are 500 gallons, and we need to put 12 tablespoons of the chem-solution in each gallon. So we multiply 500 by 12, which is 6,000. Meaning that 6,000 tablespoons of chemical solution would be needed to make the 500-gallon tank have 300 bacteria per gallon.
If y = f(x), then f⁻¹(y) = x.
We have f(x) = 2x + 2, so that f(x) = 4 when
2x + 2 = 4
2x = 2
x = 1
So we know f(1) = 4.
Then this means 1 = f⁻¹(4).
