Recall from Chapter 1 that the line through the points A and B can be described by the vector equation
for −∞ < t < ∞. Homework Help ✎
Let A = (2, 4) and B = (1, −3). Since
= 2i + 4j and = −i − 7j, verify that in this case + t( ) = 2i + 4j + t(−i − 7j).
Rewrite this expression as ( )i + ( )j.
Show that this line goes through the point (0, −10).
Use the distributive property, then combine like terms.
2i + 4j + t(−i −7j)
= 2i + 4j −ti −7tj
= 2i −ti + 4j −7tj
If (0, 10) is on the line, then 0i + 10j is possible.
(2 − t)i + (4 − 7t)j = 0i + 10j
2 − t = 0 4 − 7t = 10
Does t have the same value in both equations?
If it is on the line, then it should.