The equation relating friction `F` and the load `L` for an experiment is `F=aL+b` Measurements are taken and `F=4` when `L=6` and `F=6.5` when `L=9` Determine graphically the value of a and b

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txmedteach | High School Teacher | (Level 3) Associate Educator

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This question asks you to determine two parameters of the above equation using the points provided. Let's put things more mathematically:

`F(L) = aL+b`

Now, maybe you might recognize this bettr by substituting y for F(L) and x for L to get:

`y = ax+b`

Notice that this is the standard equation of a line! Recall, now, that we are trying to find a and b, which from the above equation will be the slope and y-intercept.

So, what we'll do to solve this graphically is to find the slope and y-intercept by plotting the two points we're given: (6,4) and (9, 6.5). We do this below:

We now draw a line between these two points:

Let's start with the y-intercept (b) because it is plainly obvious on the graph. Clearly, we see the line intercept the y-axis at -1. Therefore, our value for b is -1.

Now, to calculate the slope. We'll need to look at "rise over run." in other words, how many boxes up and then to the right do we go to get to another point? We find that for every 6 boxes to the right, we go 5 boxes up, giving us a slope of 5/6. Therefore, a = 5/6.

Hope that helps!

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