00:01
We're given a pair of points.
00:04
We're asked to find an equation of the line passing through these points and to sketch the line.
00:09
Points are 1 -1 and 6 negative 2 thirds.
00:23
To find an equation for the line, let's use the two -point form for a line.
00:31
So this says that y minus the first y component 1 over x minus the x component of the first point 1 equals the second y component negative two thirds minus first y component one over second x component six minus the first x component one.
00:56
Simplifying the right hand side, we get negative two thirds minus one is negative two thirds minus three thirds or negative five thirds.
01:06
And in the bottom we have six minus one is five.
01:11
Simplifying, we get negative one -third.
01:15
Solving for y, we have y minus 1 equals distributing the negative 1 -third, negative 1 -third x, and then negative -1 -third times negative 1 -3 is positive 1 -third.
01:30
Solving for y again, we get y equals negative 1 -third x plus 4 thirds.
01:46
To graph the line, i'll plot the two points we were given and draw a stringer.
01:50
Line between them.
01:52
So the points have x coordinates ranging from 1 to 6 and y coordinates ranging from negative 2 thirds to 1...