the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
initial value of 3, namely when x = 0, y = 3, so we have the point (0 , 3) and it has a rate or slope of 3/4.
If you know the derivative of some function
, you can tell exactly who
is, up to an additive, constant term. In fact, knowing
, you have
In your case, we have
So, the integral is almost immediate:
So, up to some constant additive term, our function is
To fix this constant, we know that the function passes through the point (6,10), so we have
And so our function is
If we want to know when this function equals 6, we simply have to ask and solve for x, so we have