? Scatter Graphs Worksheet | KS3 Maths | Beyond Secondary - Free Printable

Since I can't view or access images directly, I can't see the specific scatter plots in your worksheet. However, I can guide you through how to solve this type of problem and help you find the equations of the trend lines for each scatter plot.

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🔍 What You Need to Do:

For each scatter plot (1–10), you are asked to find the equation of the trend line (also called the line of best fit). The general form of a linear equation is:

$$
y = mx + b
$$

Where:
- $ m $ = slope of the line
- $ b $ = y-intercept

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✔ Steps to Find the Equation of the Trend Line:

#### 1. Identify Two Points on the Line
Look at the scatter plot and pick two points that lie exactly on the trend line (not just near it). These should be easy to read from the graph (e.g., where the line passes through grid intersections).

Let’s say you pick two points:
Point A: $ (x_1, y_1) $
Point B: $ (x_2, y_2) $

#### 2. Calculate the Slope ($ m $)
Use the slope formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

#### 3. Find the Y-Intercept ($ b $)
Use one of the points and plug into $ y = mx + b $, then solve for $ b $.

Example:
If $ m = 2 $, and point $ (1, 3) $ is on the line:
$$
3 = 2(1) + b \Rightarrow b = 1
$$
So the equation is $ y = 2x + 1 $

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📌 Tips:

- If the line goes up from left to right → positive slope.
- If the line goes down → negative slope.
- If the line crosses the y-axis at $ (0, b) $, that's your y-intercept.
- Use grid lines to estimate coordinates accurately.

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💡 Example Problem (Hypothetical):

Suppose Plot #1 has points at $ (0, 6) $ and $ (4, 2) $.

1. $ m = \frac{2 - 6}{4 - 0} = \frac{-4}{4} = -1 $
2. Use point $ (0, 6) $: $ y = -1x + 6 $
3. So the equation is: $ y = -x + 6 $

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🔁 Repeat This for All 10 Plots

You’ll need to do this process for each of the 10 graphs. Since I can’t see them, here’s what you should do:

1. Label the axes (usually x and y).
2. Pick two clear points on the trend line.
3. Calculate slope.
4. Find y-intercept.
5. Write the equation.

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🧩 Common Patterns:

- Some lines may have integer slopes like $ 1, 2, -1, -2 $, or fractions like $ \frac{1}{2}, -\frac{3}{4} $.
- Watch for symmetry and spacing between points.

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🛠️ Final Answer Format:

For each problem, write:
> Equation: $ y = mx + b $

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If you can describe one or two of the plots (e.g., "Plot 1 has points at (0,5), (2,3), (4,1)") — I can help you find the exact equation.

Alternatively, if you can list the coordinates of two points from each graph, I can compute all 10 equations for you.

Just let me know!