Question

how to write equation in slope-intercept form of the trend line. explain simply and numbered

Answer 1

Sure! Writing the equation of a trend line in slope-intercept form (which is \(y = mx + b\)) involves a few straightforward steps. Here's a simple guide:

### Steps to Write the Equation of a Trend Line in Slope-Intercept Form

1. **Gather Your Data Points**:
- Collect the data points you want to analyze, which are usually in the form (x, y).

2. **Plot the Data Points**:
- On a graph, plot the points for better visualization. This helps you see the trend.

3. **Find the Slope (m)**:
- Use the formula for slope:
\[
m = \frac{(y_2 - y_1)}{(x_2 - x_1)}
\]
- Choose two points (\(x_1, y_1\) and \(x_2, y_2\)) on the line to calculate the slope.

4. **Determine the Y-Intercept (b)**:
- Identify where the trend line crosses the y-axis. This value is \(b\).

5. **Write the Equation**:
- Once you have \(m\) (slope) and \(b\) (y-intercept), substitute them into the slope-intercept form:
\[
y = mx + b
\]

6. **Example**:
- If you found the slope to be \(2\) and the y-intercept to be \(3\), the equation would be:
\[
y = 2x + 3
\]

7. **Check Your Line**:
- Finally, make sure that the equation accurately represents the trend in your data by visualizing or calculating predicted values.

By following these steps, you can write the equation of a trend line in slope-intercept form!