Respuesta :
The slope of the equation is 0.50 and it interprets the additional price per minute of usage.
A cafe charges an initial fee to use the computer and then an additional price per minute of usage.
An equation representing the total cost of using a computer for t minutes at the internet cafe is given by:
C = 9 + 0.50 t
Initial fee = 9 and C = total cost and t = time usage.
What is a slope of an equation?
The process of determining the rate of change of a dependent variable
when the independent variable change is called the slope of an equation.
We can find the slope by differentiating the dependent variable with respect to the independent variable.
Slope = dy / dx
Where y = independent variable and x = dependent variable.
The given equation :
C=9+0.50t
C = dependent variable and t = independent variable.
Differentiating C with respect to t
we have,
dC / dt = d9 / dt + 0.50 dt / dt
dC / dt = 0 + 0.50. Where [tex]\frac{d}{dy} constant = 0[/tex]
dC / dt = 0.50
Slope = 0.50
Interpretation of the slope = 0.50.
The slope = 0.50 means that the additonal price per minute of usage is 0.50.
For,
t = 1, C = 9 + 0.50 = 9.5
t = 2, C = 9 + 0.50 x 2 = 9 + 1 = 10
t = 3, C = 9 + 0.50 x 3 = 9 + 1.50 = 10.50
t = 4, C = 9 + 0.50 x 4 = 9 + 2 = 11.
10 - 9.5 = 0.50
10.50 - 10 = 0.50
11 - 10.50 = 0.50
We see that the rate of change is constant which means it is 0.50 price per minute of usage.
Thus the slope of the equation is 0.50 and it interprets the additional price per minute of usage.
Learn more about slopes here:
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