Scatter plots worksheet for creating graphs and determining lines of best fit.

Here is the step-by-step solution to help you complete your scatter plot worksheet.

Part 1: Top Graph Data

Data Points: $(2, 1), (5, 5), (7, 7), (3, 3), (1, 5), (6, 2)$

Step 1: Plotting the Points
To plot these on the grid, find the $x$ number on the bottom axis and the $y$ number on the side axis.
* Point 1: Go right to $2$, go up to $1$. Mark a dot.
* Point 2: Go right to $5$, go up to $5$. Mark a dot.
* Point 3: Go right to $7$, go up to $7$. Mark a dot.
* Point 4: Go right to $3$, go up to $3$. Mark a dot.
* Point 5: Go right to $1$, go up to $5$. Mark a dot.
* Point 6: Go right to $6$, go up to $2$. Mark a dot.

Step 2: Finding the Line of Best Fit
Look at how the dots are arranged. They seem to form a straight line going upwards from left to right.
* The points $(1, 5)$ and $(6, 2)$ are a bit far away from the others (these are called outliers).
* The points $(2, 1), (3, 3), (5, 5),$ and $(7, 7)$ follow a very clear pattern: the $y$ value is almost always close to the $x$ value minus $1$ ($y = x - 1$).
* Check: If $x=2$, $y=1$. If $x=3$, $y=2$ (close to 3). If $x=5$, $y=4$ (close to 5). If $x=7$, $y=6$ (close to 7).
* Therefore, you should draw a straight line that passes through the middle of the "main group" of dots, ignoring the ones that are way off. The line should start near $(1, 0)$ or $(2, 1)$ and go up towards $(7, 6)$ or $(8, 7)$.

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Part 2: Bottom Graph Data

Data Points: $(4, 6), (6, 2), (1, 1), (3, 5), (0, 3), (2, 4)$

Step 1: Plotting the Points
* Point 1: Go right to $4$, go up to $6$. Mark a dot.
* Point 2: Go right to $6$, go up to $2$. Mark a dot.
* Point 3: Go right to $1$, go up to $1$. Mark a dot.
* Point 4: Go right to $3$, go up to $5$. Mark a dot.
* Point 5: Stay at $0$ (the vertical axis), go up to $3$. Mark a dot.
* Point 6: Go right to $2$, go up to $4$. Mark a dot.

Step 2: Finding the Line of Best Fit
Look at the shape of the dots.
* As you move to the right (higher $x$), the dots generally go down (lower $y$). This is a negative correlation.
* The point $(1, 1)$ is quite low compared to its neighbors, and $(6, 2)$ is also low.
* Most points cluster around a line that starts high on the left and goes lower on the right.
* A good line would pass somewhere between $y=5$ and $y=6$ when $x=0$, and drop down to about $y=1$ or $y=2$ when $x=6$.
* You can draw a line starting near $(0, 5.5)$ and ending near $(6, 1.5)$. It won't touch every dot, but it will cut through the middle of the cloud of dots.

Final Answer:
Top Graph:
Plot the points: (2,1), (5,5), (7,7), (3,3), (1,5), (6,2).
Draw a Line of Best Fit with a positive slope (going up from left to right). The line should pass closely through the points (2,1), (3,3), (5,5), and (7,7), effectively ignoring the outliers at (1,5) and (6,2). An approximate equation for this line is $y = x - 1$.

Bottom Graph:
Plot the points: (4,6), (6,2), (1,1), (3,5), (0,3), (2,4).
Draw a Line of Best Fit with a negative slope (going down from left to right). The line should start near the y-axis around $y=5$ or $6$ and go down towards the right, passing through the center of the data cloud, ending near $x=6, y=2$.