Discussion
Which of the following will be a point on a line that contains (−1, −1) and (2, 5)?
Answer: C
The point on the line is (100, 201).
Find the equation of the line through (−1, −1) and (2, 5).
\[ \begin{aligned} m &= \frac{5 - (-1)}{2 - (-1)} = \frac{6}{3} = 2 \\ y - 5 &= 2(x - 2) \\ y &= 2x + 1 \end{aligned} \]
For \(x = 100\), \(y = 2(100) + 1 = 201\), so (100, 201) lies on the line.
The other points fail the test: for \(x = 30\) the line gives 61, not 41; for \(x = 80\) it gives 161, not 91; and for \(x = 110\) it gives 221, not 121. Those options add 11 to \(x\), a pattern the two given points do not follow.
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