Question

Please help!!As soon as possible!!

Answer 1

Answer: Their equations have different y-intercept but the same slope

Explanation:

Since, the slope of the line passes through the points (2002,p) and (2011,q) is,

`m_1 = (q-p)/(2011-2002) = (q-p)/(9)`

Similarly, the slope of the line asses through the points (2,p) and (11,q) is,

`m_2 = (q-p)/(11-2) = (q-p)/(9)`

Since,
`m_1 = m_2`

Hence, both line have the same slope.

Now, the equation of the line one having slope
`m_1` and passes through the point (2002,p) is,

`y - p = (q-p)/(9)(x-2002)`

Put x = 0 in the above equation,

We get,
`y = (2000(p-q))/(9)+p`

The y-intercept of the line one is
`(0, (2000(p-q))/(9)+p)`

Also, the equation of second line having slope
`m_2` and passes through the point (2,p)

`y-p=(q-p)/(9)(x-2)`

Put x = 0 in the above equation,

We get,
`y = (2(p-q))/(9)+p`

The y-intercept of the line one is
`(0, (2(p-q))/(9)+p)`

Thus, both line have the different y-intercepts.

⇒ Third option is correct.