To write the equation of a line that passes through two points, you can follow these steps. Let’s take the points (1, 3) and (2, 3) as an example.
1. **Identify the Points**: We have the two points, (1, 3) and (2, 3).
2. **Calculate the Slope (m)**: The slope is calculated using the formula:
m = (y2 – y1) / (x2 – x1).
Substituting our points, we get:
m = (3 – 3) / (2 – 1) = 0 / 1 = 0.
Since the slope is 0, this tells us that the line is horizontal.
3. **Use the Point-Slope Form**: Normally, the point-slope form of a line is given by:
y – y1 = m(x – x1).
However, since our slope (m) is 0, we can rewrite this as:
y – 3 = 0(x – 1).
This simplifies to:
y = 3.
4. **Final Equation**: The final equation of the line, which is horizontal and passes through both points (1, 3) and (2, 3), is:
y = 3.
This means that for any value of x, y will always be 3, indicating a horizontal line running through the y-axis at 3.