00:01
For this problem, we're told that f of 1 .5 equals negative 5 thirds and f of 6 equals 2.
00:05
And we want to come up with the function rule or the linear function for this relationship based off these two evaluations.
00:12
And to be able to write a function in a linear relationship form, we're going to look for something that's of the form mx plus b, where if we can find the slope and the y intercept, then we can write our function rule.
00:24
And the first thing we're going to focus on is the slope, because slope is equal to y2 minus y1 over x2 minus x1.
00:34
So we were given these values in function notation form, but this is still an x and a y, and this is an x and a y, so we can find our slope by saying, let's say, y2 of 2 minus y1 of negative 5 thirds over x2 of 6 minus x1 of 1 1ā.
00:53
So we will have to do a little bit of fraction work.
00:55
This will be two plus five thirds, and two with the denominator of three would be six thirds.
01:00
So we'll end up with six thirds plus five thirds, divided by six minus one half.
01:06
Six with the denominator of two would be twelve halves.
01:08
So twelve halves minus one halves on bottom.
01:12
So when we evaluate six halves plus, or six thirds plus five thirds would give us eleven thirds.
01:19
And then twelve halves minus one half will give us eleven halves...