Option C:
is the equation that have a greater rate of change.
Explanation:
From the graph the coordinates are (0,0), (20,6), (40,12), (60,18) and (100,30)
We need to determine the rate of change.
The rate of change can be determined using the formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting the any two coordinates in the formula, we get, the slope of the equation.
Let us substitute the coordinates (20,6) and (100,30)
Thus, we have,
![m=\frac{30-6}{100-20}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B30-6%7D%7B100-20%7D)
Simplifying, we get,
![m=\frac{24}{80}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B24%7D%7B80%7D)
Dividing, we get,
![m=\frac{3}{10}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B10%7D)
Also, the y - intercept of the equation is ![b=0](https://tex.z-dn.net/?f=b%3D0)
The equation of the line becomes ![y=\frac{3}{10} x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B10%7D%20x)
Thus, the equation that has a greater rate of change is ![y=\frac{3}{10} x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B10%7D%20x)
Hence, Option C is the correct answer.