00:02
In this question, we are asked to find the values of k that make the two given lines parallel.
00:09
The first line is given in parametric vector form, and the second line is given as a single equation in x and y.
00:20
So there are two ways to solve this problem.
00:23
One is to change the first equation into a rectangular form, or to rewrite the second.
00:32
Equation in parametric vector form.
00:36
So let's rewrite the first equation in the rectangular form.
00:40
To do that we need to rewrite it as a single vector 1 plus 2s and 2 plus 3s.
00:50
Then the first coordinate is x and the second coordinate is y.
00:54
So we can rewrite it as x equals to 1 plus 2s and y equals to 2 plus 3s.
01:06
And then we can solve the first we can solve the first equation for s to get that s equals to x minus 1 over 2.
01:17
And plug in this value of s in the second equation to get y equals to 2 plus 3 multiplied by x minus 1 over 2...