Can’t see well on your scan.
Is it y = a/x^2 + b/x^1 or
y= a/x^2 + b/x’?
Im going to assume it says x^1 and not x’ since you probably aren’t doing derivatives with respect to y in middle school.
I attached an example of roughly what your graph should look like. Its not pretty because I did it on my phone but use a ruler and graph paper and it will look much better.
My steps:
1. I wrote the values of (x^2)y using the experimental values for x and y
2. We plotted 5 calculated points of (x^2)y, and drew a line from the first point to the last. The line should go through all the points if you plot them neatly enough.
3. Since y = a/x^2 + b/x,
y*x^2 = a + bx (It’s a line)
So our line can help us get a and b, we just need to approximate the slope and solve for a.
4. Approximate the slope b by calculating
b = (change in y*x^2)/(change in x)
b = (105 - 24.96)/(10-2) = 10.005
5. Use slope and any input x to solve for a: we know x^2*y = a + bx and we got b in step 4. let’s use the values we got at x = 10 to solve for a.
We know that 105 = a + 10.005(10) because of the equation above and our value of 105 = x^2*y at x= 10.
Simplifying we get 105 = a + 100.05
solve for a by subtracting 100.05 from both sides and we get
a = 4.95
