Answer:
Assuming you want an equation, y = -4/3x - 1
Step-by-step explanation:
Formula is y = mx + b
m = slope= -4/3
b = y-intercept = -1
The answer is B. When dividing exponents, you divide the coefficients and subtract the exponents from the numerator to the denominator.
So, in this case, 16/8 is 2 (eliminating C and D). Then, you subtract the exponents on r and s. For r, that’s 6-2 so the answer will be r^4. For s, that’s 3-6 so the answer will be s^-3, or 1/s^3. Put it all together and you get 2r^4/s^3, or B.
The average rate of change for this function for the interval from x = 1
to x = 3 will be 8. Therefore option B is correct.
<h3>How to find the average rate of change of something?</h3>
Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
where when
![x = x_1, y = y_1\\and \\x = x_2, y = y_2](https://tex.z-dn.net/?f=x%20%3D%20x_1%2C%20y%20%3D%20y_1%5C%5Cand%20%5C%5Cx%20%3D%20x_2%2C%20y%20%3D%20y_2)
The average rate of change can be calculated as;
From x=1 to x=3,
y = 2 and y = 18
Therefore, based on the table, when:
![x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18](https://tex.z-dn.net/?f=x_1%20%3D%201%20y_1%20%3D%202%20%5C%5Cand%20%5C%5Cx_2%20%3D%203%2C%20y_2%20%3D%2018)
Then:
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7B18%20-%202%7D%7B3-1%7D%5C%5C%5C%5C%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7B16%7D%7B2%7D%5C%5C%5C%5C%5Ctext%7BAverage%20rate%7D%20%3D%208)
Therefore option B is correct.
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