Answer: Their equations have different y-intercept but the same slope
Step-by-step explanation:
Since, the slope of the line passes through the points (2002,p) and (2011,q) is,
![m_1 = \frac{q-p}{2011-2002} = \frac{q-p}{9}](https://tex.z-dn.net/?f=m_1%20%3D%20%5Cfrac%7Bq-p%7D%7B2011-2002%7D%20%3D%20%5Cfrac%7Bq-p%7D%7B9%7D)
Similarly, the slope of the line asses through the points (2,p) and (11,q) is,
![m_2 = \frac{q-p}{11-2} = \frac{q-p}{9}](https://tex.z-dn.net/?f=m_2%20%3D%20%5Cfrac%7Bq-p%7D%7B11-2%7D%20%3D%20%5Cfrac%7Bq-p%7D%7B9%7D)
Since, ![m_1 = m_2](https://tex.z-dn.net/?f=m_1%20%3D%20m_2)
Hence, both line have the same slope.
Now, the equation of the line one having slope
and passes through the point (2002,p) is,
![y - p = \frac{q-p}{9}(x-2002)](https://tex.z-dn.net/?f=y%20-%20p%20%3D%20%5Cfrac%7Bq-p%7D%7B9%7D%28x-2002%29)
Put x = 0 in the above equation,
We get, ![y = \frac{2000(p-q)}{9}+p](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2000%28p-q%29%7D%7B9%7D%2Bp)
The y-intercept of the line one is ![(0, \frac{2000(p-q)}{9}+p)](https://tex.z-dn.net/?f=%280%2C%20%5Cfrac%7B2000%28p-q%29%7D%7B9%7D%2Bp%29)
Also, the equation of second line having slope
and passes through the point (2,p)
![y-p=\frac{q-p}{9}(x-2)](https://tex.z-dn.net/?f=y-p%3D%5Cfrac%7Bq-p%7D%7B9%7D%28x-2%29)
Put x = 0 in the above equation,
We get, ![y = \frac{2(p-q)}{9}+p](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%28p-q%29%7D%7B9%7D%2Bp)
The y-intercept of the line one is ![(0, \frac{2(p-q)}{9}+p)](https://tex.z-dn.net/?f=%280%2C%20%5Cfrac%7B2%28p-q%29%7D%7B9%7D%2Bp%29)
Thus, both line have the different y-intercepts.
⇒ Third option is correct.