What are the steps to write the equation of a line that goes through two specific points?

To find the equation of a line that passes through two points, you can follow these steps:

1. Identify the points: Let’s say the two points are (x_1, y_1) and (x_2, y_2).
2. Calculate the slope: The slope m of the line that passes through these points is calculated using the formula:
   
   m = (y_2 - y_1) / (x_2 - x_1).
   
   This slope measures the change in y for a unit change in x.
3. Use the point-slope form: With the slope m and one of the points (let’s say (x_1, y_1)), you can write the equation in point-slope form:
• y - y_1 = m(x - x_1)
4. Simplify to slope-intercept form (if desired): If you want the equation in slope-intercept form y = mx + b, you can rearrange your equation:
   
   y = mx - mx_1 + y_1
   
   Thus, your b (y-intercept) can be found as b = y_1 - mx_1. This gives you the final equation:
• y = mx + b

As an example, let’s say the points are (1, 2) and (3, 4). First, calculate the slope:

m = (4 - 2) / (3 - 1) = 2 / 2 = 1

Now, using point-slope form with the first point:

y - 2 = 1(x - 1)

Simplifying, we get:

y - 2 = x - 1
y = x + 1

Therefore, the equation of the line that passes through the points (1, 2) and (3, 4) is:

y = x + 1