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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?

graph

Astoach167
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  • well, $y$ being a linear function of $x$ means $y = a x + b$, which implies that $\Delta y = a \Delta x$. So one thing you could do is compute $\Delta y / \Delta x$ for the first $2$ points, and then for the second and third points, and check whether they are the same or not. If they are the same, then the $3$ points are collinear. Otherwise, they are not. – Malkoun Sep 22 '20 at 19:47
  • may I know what does the triangle notation means? – Astoach167 Sep 22 '20 at 20:04
  • $\Delta x$ is the change in $x$ and $\Delta y$ is the change in $y$. So for example, if you are looking at the points $(x_1,y_1)$ and $(x_2,y_2)$, then $\Delta x = x_2 - x_1$ and $\Delta y = y_2 - y_1$. – Malkoun Sep 22 '20 at 21:40

1 Answers1

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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.

grand_chat
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