Question

A line has the following vector equation.

[x, y] = [2, -3] + t[5, 1]

a) State the coordinates of three other points on the line. Can you show your work please.
b) Write another vector equation of this line.

Answer 1

a) You can use 3 different numbers for t. How about 5, 10, 20?
.. [x, y] = [2, -3] +5[5, 1] = [27, 2]
.. [x, y] = [2, -3] +10[5, 1] = [52, 7]
.. [x, y] = [2, -3] +20[5, 1] = [102, 17]


b) You can replace t with any function of whatever parametric variable you want to use. For example, t = -3s+2.
.. [x, y] = [2, -3] +(-3s +2)[5, 1]
.. = [2 -15s +10, -3 -3s +2]

.. [x, y] = [12, -1] +s[-15, -3]

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The graph uses "t" instead of "s" for the parameter of the second version of the line. This is a Desmos thing: it likes "t" for parametric equations. The second equation is shown as dotted, so you can see it is the same line as the first equation (solid red).