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To find the equation of the line with a gradient of \( 3 \) that passes through the point \( (2, 10) \), we can use the slope-intercept form of a line:

\[
y = mx + c
\]

where:
- \( m \) is the gradient (slope),
- \( c \) is the y-intercept.

### Step-by-Step Solution
1. **Identify the known values**:
   - Gradient (\( m \)) is \( 3 \).
   - The line passes through the point \( (2, 10) \).

2. **Substitute into the equation**:
   Substitute \( m = 3 \), \( x = 2 \), and \( y = 10 \) into the equation to solve for \( c \):

   \[
   10 = 3 \cdot 2 + c
   \]

3. **Calculate \( c \)**:
   \[
   10 = 6 + c
   \]
   \[
   c = 10 - 6 = 4
   \]

4. **Write the equation**:
   Now that we know \( m = 3 \) and \( c = 4 \), the equation of the line is:

   \[
   y = 3x + 4
   \]

### Final Answer
The equation of the line is:

\[
y = 3x + 4
\]

Would you like a more detailed breakdown or have any questions?

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### Related Questions
1. How would the equation change if the line passed through a different point with the same gradient?
2. What is the equation of a line with a gradient of -3 that passes through the point (2, 10)?
3. How can we find the equation of a line if we know two points on the line instead of the gradient?
4. How would the equation look if the line was parallel to \( y = 3x + 4 \) but had a different y-intercept?
5. What are some real-life examples where calculating the equation of a line is useful?

### Tip
Remember, you can always find the y-intercept by plugging in the coordinates of a known point on the line into the equation \( y = mx + c \).

A straight line has a gradient of 3 and passes through the point (2, 10). Work out the equation of the line. Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.

Learn how to find the equation of a line with a gradient of 3 that passes through the point (2, 10). This problem demonstrates the use of the slope-intercept form (y = mx + c) and is suitable for students in Grades 8-10.

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