00:01
For this problem, we are given that f of x is equal to the square root of x, and we are asked to find the equation of the secant line, passing through points 4, 2, and points 5, and f of 5.
00:14
So we're given one coordinate, and we are also given another coordinate in a slightly different form.
00:21
So the first thing we need to do is plug in 5 for our x value to get what our y value will be.
00:30
So we have f of 5 is equal to the square root of 5.
00:36
And unfortunately, that doesn't really come out to a nice number.
00:40
So we're going to leave it like that.
00:42
Now we're asked to find the secant line passing through this line.
00:47
So let's remind ourselves, just generically speaking, the equation of a line with point slope.
00:53
So we have y minus y 1.
00:55
It's equal to m times x minus x1.
01:00
And so here we only need one point and then we need a slope.
01:08
Since we have two points, we can just choose one of those to plug in for our y1 and x1.
01:13
But we do need to find the slope of this line.
01:19
So remember that slope is equal to y2 minus y1 all over x2 minus x1.
01:30
So that's our rise over run.
01:33
Again, we have two points here, so we can just plug those in.
01:38
I'm going to take this as my x2y2, and this is going to be my x1y1.
01:49
So with that in mind, we have our square root of 5 minus 2, all over 5 minus 4.
01:59
It's going to come out to 1 on the bottom.
02:02
So we get not really a super nice number, negative 2 plus square root of 5.
02:09
And that does come out to approximately 0 .236 is going to be what our slope is.
02:23
So now that we have our slope and we have a point, we're going to go ahead and just choose to use the point for 2 .2.
02:34
To make things easier.
02:36
So we have y minus 2, which is equal to.
02:41
We'll just go ahead and leave it in this form...