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,
[tex]m_1 = \frac{q-p}{2011-2002} = \frac{q-p}{9}[/tex]
Similarly, the slope of the line asses through the points (2,p) and (11,q) is,
[tex]m_2 = \frac{q-p}{11-2} = \frac{q-p}{9}[/tex]
Since, [tex]m_1 = m_2[/tex]
Hence, both line have the same slope.
Now, the equation of the line one having slope [tex]m_1[/tex] and passes through the point (2002,p) is,
[tex]y - p = \frac{q-p}{9}(x-2002)[/tex]
Put x = 0 in the above equation,
We get, [tex]y = \frac{2000(p-q)}{9}+p[/tex]
The y-intercept of the line one is [tex](0, \frac{2000(p-q)}{9}+p)[/tex]
Also, the equation of second line having slope [tex]m_2[/tex] and passes through the point (2,p)
[tex]y-p=\frac{q-p}{9}(x-2)[/tex]
Put x = 0 in the above equation,
We get, [tex]y = \frac{2(p-q)}{9}+p[/tex]
The y-intercept of the line one is [tex](0, \frac{2(p-q)}{9}+p)[/tex]
Thus, both line have the different y-intercepts.
⇒ Third option is correct.
