Part (a)
Open up Desmos and click on the button that looks like a plus sign. It's at the upper left corner. We're going to want to add a table.
Type all of the values into the table. This table is stacked vertically compared to yours which is laid out horizontally. It's the same thing pretty much. It depends on your preference on which you like better.
After the data values are typed in (which is a bit of a tedious process if you ask me), you'll then move to the next input box to type the following
Type it in exactly as you see it. To get the small '1's as subscripts, you'll need to use an underscore. So you'll type y_1 to mean
The ~ symbol is likely found in the upper left portion of your keyboard.
After typing that into the second input box, you should get what you see in the screenshot below.
The parameters your teacher wants are the m and b values.
Desmos is showing these values:
These values are approximate. As the instructions state, do not round the values mentioned.
Therefore, we go from y = mx+b to y = 0.125873x-7.11916 approximately
This is the regression line. It is the closest line to all of the points.
Answer: y = 0.125873x-7.11916
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Part (b)
The year 2022 is 2022-1900 = 122 years after the year 1900.
This means we'll plug x = 122 into the regression equation to find the predicted value for y.
y = 0.125873x-7.11916
y = 0.125873*122-7.11916
y = 8.237346
I used the Desmos input box as a calculator. Simply type in 0.125873*122-7.11916 exactly as you see it and it should produce the value 8.237346
That then rounds to 8.24
We predict in the year 2022, the minimum wage should be about $8.24
This is an estimated value because the regression line isn't perfect. In fact, the further we move away from the main known points, the worse off the estimation will likely get. This is why extrapolation could be a bad idea. However, it's a fairly good way to see what's going on.
Answer: $8.24