The following graph is linear and has the equation: 2x + 3 = y. I am trying to follow this tutorial video:https://www.youtube.com/watch?v=YORfLpnppOU&ab_channel=AnilKumar to figure out the equation I mentioned if in the first place I don't know the equation and am given 3 points: (1,5), (2, 7), (2.5, 8), but I got stuck when applying what he said:
7-5 = 2
8-7 = 1
so this means that the difference is not constant so its not a linear graph, but that is impossible since the graph is linear. Can someone tell me what is wrong?
The rule being discussed in the video applies when the $x$ values are equally spaced. If you have a linear graph, then equally spaced $x$ values will correspond to $y$ values that are also equally spaced (with different spacing, usually), so the differences in those $y$ values will be constant.
In your problem the $x$ values are not equally spaced. This is the reason why you reach the wrong conclusion when applying the methods of the video.